Can matter possess infinite potential energy?

Can Matter Possess Infinite Potential Energy?
Can matter possess infinite potential energy? Image link: https://en.wikipedia.org/wiki/Double-slit_experiment
C O N T E N T S:

KEY TOPICS

  • If a body A is at infinite distance from another body B, it has zero gravitational potential energy, but if it is at “zero” distance from another body B, it has negative infinite potential energy, and acquires infinite kinetic energy in the process of getting there.(More…)
  • There are infinite potential possibilities for that energy to take shape.(More…)

POSSIBLY USEFUL

  • Many physical processes cause energy to be converted from potential to kinetic or the reverse, and from energy to mass or the reverse.(More…)
  • Meaning these particles, or atoms, will only take shape when we place our attention on them; otherwise, they return to their original state of pure energy and potential.(More…)
  • Kinetic Energy and Work (W AK) Question: A skier of mass 65.0 kg is on an incline of 15.0 degrees, and has an initial velocity down the incline of 5.00 m/s.(More…)
  • Considering the universe to be approximately uniform, one can show that the total negative gravitational energy in it would exactly cancel out the total positive energy represented by matter.(More…)

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KEY TOPICS

If a body A is at infinite distance from another body B, it has zero gravitational potential energy, but if it is at “zero” distance from another body B, it has negative infinite potential energy, and acquires infinite kinetic energy in the process of getting there. [1]

Now, in this model, we first assume that the particle has zero potential energy and is bound in a well with barriers of infinite potential energy. [2] Figure 1 : depiction of a particle (a) and wave (b) confined to a well with barriers of infinite potential energy. [2]

First off, your approach of having the potential be zero when the distance between the object is zero, and infinite as it approaches infinite distance has a flat: this would make the potential energy of any two objects at any finite distance infinite. [1]

As the objects move farther and farther away their potential energy increases towards zero, but this is not very important; what matters is that the curve becomes flatter. [1] What matters is not how much potential energy a body has, but whether it could have less by moving somewhere else. [1]

The object has zero net energy — positive kinetic energy $E_k$ and negative gravitational potential energy $E_p$ are equal. [3] For this condition to be met, the Big Bang would have to create the universe with an exact balance between positive mass-energy and negative gravitational potential energy, so the total mass-energy is equal to zero. [3] It’s true that the zero point of potential energy is arbitrary, but the gravitational potential function for a point mass is singular at $r0$, so that’s the one place where you can’t define the gravitational potential to be zero (or anything else – the potential function is undefined here). [1] As a mass moves in a gravitational field, it typically exchanges kinetic and potential energy. [3]

The Fermi energy can only be defined for non-interacting fermions (where the potential energy or band edge is a static, well defined quantity), whereas the Fermi level (the electrochemical potential of an electron) remains well defined even in complex interacting systems, at thermodynamic equilibrium. [4] The Fermi energy is an energy difference (usually corresponding to a kinetic energy ), whereas the Fermi level is a total energy level including kinetic energy and potential energy. [4] Remember that equation (14) provides the total energy of an orbiting body, the sum of positive kinetic and negative potential energy. [3] Notice the minus sign in equation (4) above — it means that gravitational potential energy is negative. [3] Equation (7) tell us that negative gravitational potential energy is the correct physical interpretation, and it arises from mathematics, not an arbitrary choice or convention. [3] It turns out that, for circular orbits, the relationship between kinetic and potential energy is fixed, regardless of the orbit’s other properties — the negative gravitational potential energy is always twice the magnitude of the positive kinetic energy. [3] In the standard convention, the gravitational potential between two bodies is negative, and by moving closer this potential energy will be more negative; the energy lost is converted into kinetic energy. [1] @user1648764 In the final configuration with extra kinetic energy, the gravitational potential energy will be more negative than it was at the beginning. [1] If you want to be safe, then replace your point masses with little grains of sand or dust or something, so your statement becomes “if it is touching another body B, it has negative potential energy $-U$, and acquires kinetic energy $U$ in the process of getting there.” [1] What is the difference between potential and kinetic energy such that kinetic energy cannot have any chosen reference point and cannot be negative, but potential energy can be? Both are energies and both are equally real. [1] The pendulum’s potential energy has the reverse relationship — it increases (i.e. becomes less negative) with distance from the center of the earth, and in exchange, the kinetic energy must decrease. [3]

Figure 2: Depiction of the wave behavior of a particle with energy, E, in a Finite Well with a finite potential energy, V, equal to a constant, P. [2] What distinguishes the Finite Well from the Particle in a Box scenarios are that for the finite well, the potential energy, V, of the barriers do not approach infinity. [2] Now, for the regions outside the well, the particle may have energy that is greater than or less than the potential energy of the well. [2] In each of the cases examined so far — the pendulum as well as the elliptical and circular orbits — the sum of energies has been negative, dominated by negative gravitational potential energy. [3] This final objection is answered by the idea expressed in this article — if the universe began with an exact balance between positive mass-energy and negative gravitational potential energy, the law of mass-energy conservation is honored. [3] Its (negative) potential energy results from its altitude above the center of mass of the body it orbits. [3] This doesn’t mean the object’s velocity will remain the same, nor does it mean the object’s kinetic and potential energy values will remain the same. [3] It means the total energy, the sum of kinetic and potential energy, will remain the same. [3] I chose this configuration to show that, even though there is an ongoing exchange between kinetic and potential energy, as with the pendulum the total energy remains constant. [3] The swinging pendulum in Figure 2 shows this — even though there is a periodic exchange between kinetic and potential energy, the total energy ($E_p + E_k$) is constant. [3] The potential energy may be in debt but the kinetic energy is not, and the total energy remains constant. [1] Given the total energy is conserved, that energy can be converted between potential and kinetic, that the potential energy is $0$ at infinity, and that the masses would gain kinetic energy through their mutual attraction, it follows that this gain in kinetic energy – a quantity that is classically non-negative – must be at the expense of the potential energy. [1] If we want to convert any more of the gravitational potential energy into kinetic energy, we need to dig a hole. [1] The first gravitational potential energy equation we learn is $Emgh$. [1] For small-scale mechanical systems like the pendulum, it’s convenient to establish an arbitrary zero point for potential energy. [3] The zero point is set at the bottom of the swing, so potential energy is pictured as increasing from zero to positive values as the pendulum swings. [3] Your mistake is in assuming that the value of potential energy is relevant, like when you say that if two bodies don’t interact there should be zero potential energy. [1] Potential energy is simply a function of position which is defined in such a way that as long as the associated force is the only one doing work on the body, then the combination $EKE + PE$ remains constant. [1] They would lose less potential energy by moving a fixed distance, so the force is smaller. [1] Because we know that potential energy reduces with height (with distance between the objects). [1] It just means astronomers don’t get to assume that an object runs out of potential energy at PE0. [1] Saying a rock at the top of the cliff has potential energy just means it will gain kinetic energy if you drop it over the edge. [1] Unless the mentioned amount of potential energy really exists, it cannot be converted to kinetic energy. [1] Potential energy is the energy of a specific type that would be involved if a specific state change occurs. [1] Potential energy is the energy of position or state — examples might be a book on a high shelf or a charged battery. [3] Now let’s look at the relationship between an orbit’s kinetic and potential energy. [3] This is a reasonable way to picture a physical system, but the absolute value of gravitational potential energy is typically a much larger value, and is always negative. [3] The constant can be selected such that the potential energy at some positions are negative. [1] Saying a rock at the bottom of the cliff has negative potential energy just means it will take at least a certain amount of energy to get it up to the top of the cliff (and it’s interesting that that’s about the same energy (minus friction) you get from dropping the same rock back down). [1] What value does the potential energy have now? Is it negative? Yes it is. [1] For the region between x0 and xL, we have a potential energy, V, equal to zero. [2] The physical thing is the potential energy difference between two points in space, not the actual value of the potential energy at any particular point. [1] Because objects always want to move towards a situation of lower potential energy. [1] @user1648764 : Gravitational potential energy is not stored in bodies. [1] There is no process at all that can measure the absolute gravitational potential energy of a body. [1]

There are infinite potential possibilities for that energy to take shape. [5] I found and animation who says that the energy is negative because the eletrical potential energy turns in to kinect energy, and the zero at infinite distance is only a referencial. [6]

The absolute value of the potential energy does not matter, what governs the dynamical behavior of a system is the gradient of the potential energy which is proportional to a force. [6] In the minimum of a potential energy curve, the gradient is zero and thus the net force is zero – the particles are stable. [6] Probably in that video some kind of agreement must have been made with the reader that the initial potential energy is zero, because if they later on mentioned that the potential energy becomes negative, that is the same as saying that the potential energy has decreased. [6] The difference between this constant line and the potential energy below it at each point gives the kinetic energy at that point (E EK + EP). [6] The potential energy will not infinitely increase when the atoms are stretched. [6] When the atom configuration is in such way so that the potential energy is minimum for this system. [6] Conservative force like the one relevant in this case is equal to the gradient of potential energy. [6] This is precisely why blue_leaf77 said that the gradient of the potential energy curve provides the information of how the force is in this molecule. [6] Its not quite right to assign charges for the molecules in question because in fact that potential energy curve is not obtained using the usual electrostatic potential energy formula. [6] It just happens that the ground state energy of H 2 molecule so obtained takes a shape that resembles electrostatic potential energy. [6] If quartz (in the form of sand) is melted and allowed to cool, it becomes so viscous that the molecules are unable to move to the low potential energy positions they would occupy in the crystal lattice, so that the disorder present in the liquid gets “frozen into” the solid. [7] Where do you think the marble will go? It will eventually roll to the equilibrium position, right? That is what the potential energy means, and what the figure means. [6] In our case, we can set x as r 2, so we should get a quadratic potential energy like shown in the grey dotted line in the figure. [6] This is why, the actual potential energy looks like the solid black line in the figure. [6] In a solid comprised of identical molecular units, the most favored (lowest potential energy) locations occur at regular intervals in space. [7]

Professors Barton Beebe and Jeanne Fromer?s empirical tour de force presents a strong challenge to the conventional wisdom that there are infinite potential trademarks. 1 × 1. [8] None of those potential possibilities will actually take shape unless and until we focus our attention on one (or more) of these infinite potential possibilities. [5]

The real problem here is that the potential walls are infinitely high and if you instantaneously move the wall to the center then there is half of the original wave function outside the well at t 0, and this is forbidden due to the height of the wall being infinite and so the implication is that an infinite amount of work has been done to get some of the wave function in that forbidden region; this means, of course, the particle now has infinite energy. [9] For total energy E less than zero, corresponding to bound states in hydrogen?s potential well, most solutions become infinite at large r and therefore aren?t normalizable. r As a result, only certain values of the energy E give acceptable bound-state solutions. [10]

For our purposes here, I am going to set the potential energy equal to zero where the two objects are when they are at rest; therefore, these two particles have a total energy of zero. [9] A particle of mass m is in a region where its total energy E is less than its potential energy U. Show that the Schringer equation a much more concentrated energy source than fossil fuels, whose has nonzero solutions of the form Ae612m1U2E2x/”. [10] In order to de- 53. (a) Using the potential energy U 5 2 mv2x2 discussed on page 635, termine the spring constant in your model, you measure the minimum photon energy that will promote HCl molecules to develop the Schringer equation for the harmonic oscillator. their first excited state. [10] If an object falls from one point to another point inside a gravitational field, the force of gravity will do positive work on the object, and the gravitational potential energy will decrease by the same amount. [11] Gravitational energy is the potential energy associated with gravitational force, as work is required to elevate objects against Earth’s gravity. [11]

How does an object having mass, such as a pencil at rest, store that much potential energy? I understand that an object in motion has kinetic energy. [9] If the book falls off the table, this potential energy goes to accelerate the mass of the book and is converted into kinetic energy. [11] The factors that affect an object’s gravitational potential energy are its height relative to some reference point, its mass, and the strength of the gravitational field it is in. [11] ANSWER: It is not a question of the mass “storing up” potential energy. [9] ANSWER: The roller coaster and the basketball are analogous because there is kinetic energy and gravitational potential energy only in each case. [9] Then if one of these particles drifts closer, such that it cannot escape the gravitational pull between them, then suddenly the potential energy would be quite significant. [9] I guess what I mean is that at some great distance between two objects, at some great distance this potential energy will be essentially zero. [9] ANSWER: First choose potential energy to be zero at the bottom. [9] Total Equilibrium At equilibrium the potential energy is a minimum (Fig. 37.11), corresponding to zero net -1 force on the ion. [10] Chlorine, at the opposite end of the periodic table, has such a strong electron affinity that the energy of a Cl2 ion is actually 3.8 eV below that of a neutral Cl FIGURE 37.1 Potential energy of a pair of hydro- atom. [10] Because they?ve moved with the electric field, the electrons that have diffused into the P-type region have higher potential energy than those that remained behind in the N-type region. (Remember that electrons are negative, so their potential energy increases when they move in the same direction as an electric field.) [10] Electrons can only travel in discrete orbits at specific distances from the nucleus and contain a specific amount of potential energy; they can only gain or lose energy by jumping to a higher or lower orbit. [12] QUESTION: I have a question about finding the distance that a spring has been stretch using Hooke’s Law vs. conservation of energy and the elastic potential energy equation. [9] We can therefore use Equation 36.1 as the potential energy in the Schringer equation for the hydrogen atom. [10] When you compress a spring you cause the atoms to be more closely spaced than they “want to be” and it takes work to scrunch them up like that, hence the potential energy. [9] Because the electron?s potential energy depends on radial distance r, it?s best to work in spherical coordinates, where the position of a point is given by its distance r from the ori- gin along with two angles u and f that specify its orientation (Fig. 36.1). [10] ANSWER: The potential energy has its origins at the atomic level. [9] I can also determing the distanced stretched by determining the energy stored through gravitational potential energy before the mass settles and transferring it to energy stored through elastical energy after the mass settles. [9] The thing that makes it harder is that potential energy will also include gravitational potential energy mgh because the height of the object varies during the launch time; also, the location where the projectile leaves the platform will not be when the spring is unstretched. [9] An object at a certain height above the Moon’s surface has less gravitational potential energy than at the same height above the Earth’s surface because the Moon’s gravity is weaker. [11] Since the gravitational potential energy (near the earth’s surface) is simply mgy, the greater y is the greater potential energy is; therefore the kinetic energy is smallest (neglecting frictional effects) at the top of the path. [9] Because of energy conservation, they must therefore acquire a negative potential energy equal in magnitude to the (positive) kinetic energy. [9] This will show up in all the forms you suggest: sound, increased temperature of parts of the system, kinetic energy of all the fragments and the ball, and increased potential energy due to the broken bonds previously holding the vase together. [9] The ball starts with all potential energy, converts it to kinetic energy as it falls, and ends with all kinetic energy. [9] And, no, all potential energy need not be converted to kinetic energy although it could be. [9] If you include the earth in the system, the kinetic and potential energy will remain constant in the absence of any air resistance. [9] Use these values and the Madelung constant a 5 1.748 U0r0 21 to find the exponent n in Equation 37.4 for NaCl. ake2 n 5 a1 1 b 5 8.22 INTERPRET Here we?re given all but one of the quantities in the ex- pression for a crystal?s potential energy, and we?re asked to solve for with k the constant in Coulomb?s law and e the elementary charge; the one unknown, n. other quantities are given in the problem statement. [10] Note that “height” in the common sense of the term cannot be used for gravitational potential energy calculations when gravity is not assumed to be a constant. [11] Trebuchet : A trebuchet uses the gravitational potential energy of the counterweight to throw projectiles over long distances. [11] Then there are 12 sodium ions a distance 12r from the sodium; they give rise to a repulsive force and consequently a positive potential energy 112ke2/ 12r. [10] This is what potential energy is; note that it presents a way to internalize the work done by a force (weight in this case) so you never have to calculate the work done by that force again. [9] I know that EMC^2 tells one that maximum potential energy within a unit of mass. [9] The diving board, however, is a different situation because the diving board is like a spring, that is when it is bent just before the dive it too has potential energy; so, for example, as the diver starts up from the position of maximum flex, the gravitational potential energy will be increaseing and the spring potential energy will be decreasing. [9] The potential energy due to elevated positions is called gravitational potential energy, and is evidenced by water in an elevated reservoir or kept behind a dam. [11] I assume each twist raises the seat and hence the gravitational potential energy, so why does it make multiple twists? My guess is it is something to do with the coil in the rope. [9] A book lying on a table has less gravitational potential energy than the same book on top of a taller cupboard, and less gravitational potential energy than a heavier book lying on the same table. [11] As you suggest, the potential energy is very small (but not exactly zero). [9] One of the things about potential energy is that the value is not important, you may set it equal to zero anywhere, but it is usually set equal to zero when the two are infinitely far apart. [9] ANSWER: You cannot judge how fast something will go by its potential energy. [9] We treat the massive proton as being at rest at the origin, so Equation 36.1 gives the elec- tron?s potential energy as a function of radial position r. [10] DEVELOP Equation 37.4 for the potential energy U looks formidable, ASSESS The large value of this exponent shows that the NaCl crystal with n in two places, including an exponent. [10] The potential energy of a singly ionized positive sodium ion in the potential of each negative chlorine ion is 2ke2/r. [10] If the weight is lifted 1 foot, then you have done 50 ft-lb of work on it, increased its potential energy by 50 ft-lb. [9]

Your “mirror”, which I presume is an infinite potential barrier on either side cannot instantaneously drop in without doing infinite work for the same reason the wall cannot move instantaneously in. [9] You are more than your experiences, and an infinite potential of possibility awaits you as you allow your identity to evolve. [13]

Let’s slightly change your question and ask whether the acceleration at 30,000 ft would be larger than the acceleration at the surface of the earth because the potential energy is larger up there. [9] This repulsion is described approximately by a potential energy of the form U2 5 A/rn, where A and n are constants. [10]

The gravitational potential energy which keeps two pieces of matter in contact with one another must be negative since it takes positive energy to pull them apart. [14] In physics, escape velocity is the speed of an object at which its kinetic energy is equal to the magnitude of its gravitational potential energy, as calculated by the equation. [15] This corresponds to the fact that the potential energy with respect to infinity of an object in such an orbit is minus two times its kinetic energy, while to escape the sum of potential and kinetic energy needs to be at least zero. [15] For an object with a given total energy, which is moving subject to conservative forces (such as a static gravity fields) the object can reach only combinations of places and speeds which have that total energy; and places which have a higher potential energy than this cannot be reached at all. [15] For a given gravitational potential energy at a given position, the escape velocity is the minimum speed an object without propulsion needs to have sufficient energy to be able to “escape” from the gravity, that is, so that gravity will never manage to pull it back. [15] The escape velocity from a position in a field with multiple sources is derived from the total potential energy per kg at that position, relative to infinity. [15]

Utilizing the creational template of Metatron?s Cube enhances the formation of ordered vortex phenomenon and the subsequent materialization of the torus merkaba as a hyperdimensional vehicle to access the quantum field of infinite potential. [16] In Aristotelian thought, we have a spectrum: at one pole we have “dumb” prima materia, with infinite potential but zero actualization; at the other pole, God, with all actualization and zero potential. [17] Because it lacks all form, prima materia possesses infinite potential, e.g., the potential to become anything whatsoever when properly informed. [17] It is a rare moment of galactic equilibrium, the gate is opening to infinite potential. [16]

Corresponding changes in the mean potential energy were calculated by direct method and by thermodynamic integration. [18]

POSSIBLY USEFUL

Many physical processes cause energy to be converted from potential to kinetic or the reverse, and from energy to mass or the reverse. [3] Another way to say this is that, for a circular orbit, 2/3 of the energy is negative potential and 1/3 is positive kinetic. [3] As universe expands without limit, dark/vacuum energies are created too so is the energy that can be created (potential energy/potentiality) i. [19]

It has been recently suggested that, if the Big Bang could impart escape velocity to the universe’s matter — thus balancing positive and negative energy — a random quantum fluctuation could have brought the universe into existence. [3] Therefore escape velocity is the only case where, at an infinite time and distance, an object possesses zero energy and achieves zero velocity. [3] Now that we have solved for the Energy of a particle in an infinite well, we can return to solving for the wavefunction Ψ(x). [2] Derive the wavefunction, Ψ, and energy, E, for the Particle in a 1 dimensional box (infinite well), while describing any conditions that must be imposed on the wavefunction. [2]

By restricting the particle to portential wells, we are able to derive the particle’s wavefunction–both inside and outside of the well–and the quantum mechanical energy that the particle possesses due to its wave-like behavior. [2] An uncertainty in energy, for a particle, means there must be an uncertainty inherent in its mass, too, since E mc 2. [20] Bubble chamber tracks from Fermilab, revealing the charge, mass, energy and momentum of the particles created. [20] If it has a bigger energy uncertainty, it has a bigger mass uncertainty, and the shorter-lived a particle is, the bigger its mass uncertainty has to be. [20] Since bosons with the same energy can occupy the same place in space, bosons are often force carrier particles, including composite bosons such as mesons. [21] Unless acted on by an external force, an object moving in space will maintain a constant energy. [3]

A more in-depth analysis of Equation 3.2, which is beyond the scope of this module, allows for a derivation of the energy of an electron in a Hydrogen atom. [2] At this point, those sufficiently adept at mathematics will compare equations (13) (escape velocity) and (14) (total energy) and a light bulb will go off. [3] Obviously we might select a very high velocity and produce a positive result for equation (10) above, the total orbital energy. [3]

We can, however, make use of our result in the derivations for the Particle in a Box to obtain a formula for the Energy of a particle in a Finite Well. [2] To find the ground state of the whole system, we start with an empty system, and add particles one at a time, consecutively filling up the unoccupied stationary states with the lowest energy. [4] Every time you create a Higgs particle, it could be (in terms of energy) 124.5 GeV, 125.0 GeV, 125.5 GeV, or 126.0 GeV, or anywhere in between. [20] This means that, literally, when you create one of these particles and measure how much energy it had, it’s fundamentally and inherently different than the next particle of exactly the same type you’ll create. [20] This is not the case for more complex atoms, whose energy also depends on the angular momentum quantum number, \(l\). [2] In this article we’ll explore the relationship between gravity and energy, and consider some consequences for matters both large and small. [3] Expansion velocity is less than escape velocity, negative gravitational energy predominates, space is positively curved, expansion will reverse and the universe will eventually collapse. [3] Q.E.D. An object given escape velocity will have zero orbital energy, and very important, this is only true at escape velocity, no other. [3] Is there an orbital velocity that exactly balances the two kinds of energy and produces zero? Yes, there is — it’s called escape velocity. [3] Because of its importance to what follows, we should prove that escape velocity results in zero net energy (i.e. $E_k$ + $E_p$ 0). [3] As a consequence, even if we have extracted all possible energy from a Fermi gas by cooling it to near absolute zero temperature, the fermions are still moving around at a high speed. [4]

Calculate the energy of an electron in a well that is 1 Å long. [2] That means there’s an inherent uncertainty to its energy as well; using our uncertainty formula, it tells us that if you multiply your energy uncertainty (? E ) by your time uncertainty ( ? t ), it has to be greater than or equal to ?/2. [20]

If you have a large uncertainty in energy (?E), the lifetime (?t) of the particle(s) created must be very short. [20] These stationary states will typically be distinct in energy. [4] In modern physics, mass and energy are complementary aspects of a fundamental quantity that, for lack of a better word, we call mass-energy. [3] Electrons accept the exciting energy from a chemical reaction that. [22] Although the entire process was computationally complex, it allowed the scientists to combine the strengths of complementary methods and determine the energy per atom to a high degree of accuracy. [22] The recent discovery of Dark Energy as an acceleration term in universal expansion doesn’t change the physics for that era because positive mass-energy and negative gravitational energy were both much larger factors than dark energy. [3] The above table suggests that, if space is classically flat or Cartesian, this supports the zero-energy condition required for the Big Bang to create the universe without violating energy conservation. [3] Calculate the ground state energy of a baseball that weighs 145 grams that is in a football field 100 yards long. [2]

The equations for the kinetic energy of an in-falling particle become infinite at the center, just as the equation for electrostatic force becomes infinite at zero distance from an electron. [19] When a gas of Bose particles is cooled down to temperatures very close to absolute zero, then the kinetic energy of the particles decreases to a negligible amount, and they condense into the lowest energy level state. [21] Since the Fermi level in a metal at absolute zero is the energy of the highest occupied single particle state, then the Fermi energy in a metal is the energy difference between the Fermi level and lowest occupied single-particle state, at zero-temperature. [4]

A spatially-delocalized state (i.e. with low ( x ) ) is preferable: if the number density of the condensate is about the same as in ordinary liquid or solid state, then the repulsive potential for the N -particle condensate in such state can be no higher than for a liquid or a crystalline lattice of the same N particles described without quantum statistics. [21] The solutions to the Infinite Well and Finite Well are useful for describing the behavior of a particle when confined to a small region of space with large and small potential barriers, respectively. [2] Symmetric wavefunction for a (bosonic) 2-particle state in an infinite square well potential. [21]

Aside of statistics, bosons can interact – for example, helium-4 atoms are repulsed by intermolecular force on a very close approach, and if one hypothesizes their condensation in a spatially-localized state, then gains from the statistics cannot overcome a prohibitive force potential. [21] A UNSW study published this week resolves key challenges in creation of hole-based artificial atoms, with excellent potential for more-stable, faster, more scalable quantum computing. [22]

The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. [21]

Bosons are particles which obey Bose-Einstein statistics: When one swaps two bosons (of the same species), the wavefunction of the system is unchanged. 12 Fermions, on the other hand, obey Fermi-Dirac statistics and the Pauli exclusion principle: Two fermions cannot occupy the same quantum state, accounting for the “rigidity” or “stiffness” of matter which includes fermions. [21] If a particle is completely stable, then the uncertainty in its lifetime doesn’t really matter: any finite uncertainty ( ? t ) added on to an infinite lifetime is inconsequential. [20] By solving the Schrödinger Equation for the Infinite Well, Finite Well, and the Hydrogen Atom, we are able to establish models that allow for a good understanding of the behavior of a particle when confined to a small region of space, whose length is proportional to the Planck wavelength of the particle. [2] Several different models have been developed that provide a means by which to study a matter-wave when confined to a small region: the particle in a box (infinite well), finite well, and the Hydrogen atom. [2]

Find the probability that an electron in the n2 state of an infinite well (1 Å long) is found between xL/4 and x3L/4. [2] These are basically any systems that–like an infinite chain of hydrogen atoms — contain large numbers of atoms or molecules, and, therefore, many electrons. [22]

At an infinite distance, an escape-velocity object will achieve zero velocity. [3]

Whereas the elementary particles that make up matter (i.e. leptons and quarks ) are fermions, the elementary bosons are force carriers that function as the ‘glue’ holding matter together. 11 This property holds for all particles with integer spin (s 0, 1, 2, etc.) as a consequence of the spin-statistics theorem. [21] Fermions are sometimes said to be the constituents of matter, while bosons are said to be the particles that transmit interactions (force carriers), or the constituents of radiation. [21] Bose-Einstein statistics for a material particle is not a mechanism to bypass physical restrictions on the density of the corresponding substance, and superfluid liquid helium has a density comparable to the density of ordinary liquid matter. [21] ISBN 978-1598033502. boson: A force-carrying particle, as opposed to a matter particle (fermion). [21] In most applications of the wave behavior of matter, we are only interested in the probability of finding the particle in a particular region. [2]

It is a simple matter of statistics — the probability of a macroscopic quantum effect is inversely proportional to the mass under consideration. [3] Well, no — quantum effects are a matter of probability, not possibility. [3] While electromagnetic radiation were well understood to obey Maxwell’s Equations, matter obeyed no known equations. [2]

They expect that the data will be useful for analyzing the computational methods, benchmarking new methods, studying other many-electron systems, and gaining a deeper understanding of many areas throughout condensed matter physics, quantum chemistry, and materials science, among other fields. [22] Fermions are usually associated with matter (although in quantum mechanics the distinction between the two concepts is not clearcut). [21]

It turns out there is a relationship between the average velocity of matter in the expanding universe, and the overall curvature of spacetime. [3] In classical physics, all variables commute: it doesn’t matter whether you measure position and then momentum, or momentum and then position. [20] Therefore the Big Bang would have to give matter an initial velocity exactly equal to escape velocity. [3]

When all the particles have been put in, the Fermi energy is the kinetic energy of the highest occupied state. [4] In a Fermi gas, the lowest occupied state is taken to have zero kinetic energy, whereas in a metal, the lowest occupied state is typically taken to mean the bottom of the conduction band. [4] The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. [4] The Fermi energy is only defined at absolute zero, while the Fermi level is defined for any temperature. [4]

Spatially-delocalized states also permit for a low momentum according to the uncertainty principle, hence for low kinetic energy ; this is why superfluidity and superconductivity are usually observed in low temperatures. [21] A swinging pendulum (Figure 2) has maximum kinetic energy at the lowest point in its swing, and zero kinetic energy at the highest. [3] ” (emphasis mine) and later “Members of the academic establishment were quick to point out that kinetic energy is clearly not conserved.” [1]

The fastest ones are moving at a velocity corresponding to a kinetic energy equal to the Fermi energy. [4] Its (positive) kinetic energy results from its orbital velocity. [3] Kinetic energy is the energy of an object’s actual current relative velocity. [1]

Expansion velocity is equal to escape velocity, total energy is equal to zero, space is flat or classically Cartesian, expansion velocity will decrease asymptotically and reach zero at infinity. [3] The total energy represented by a black hole is finite, because its total mass is finite. [19]

The Fermi energy is an important concept in the solid state physics of metals and superconductors. [4]

The side effect is that all potential energies here are negative, as you noticed. [1] We can talk about any number of potential imaginary possible scenarios. [1]

Because the wavefunction is limited in the confines of the infinite well, the wavenumber, k, can only take on certain discrete values that would allow Ψ(0)0 and Ψ(L)0. [2]

Meaning these particles, or atoms, will only take shape when we place our attention on them; otherwise, they return to their original state of pure energy and potential. [5] The matter of these carriers is degenerate, so their constituent particles are in quantum states with nearly the same energy, and therefore the states of such matter are described by the laws of quantum mechanics. [23] Quantum physicists discovered that a person observing the infinitesimals particles of an atom actually affects the behavior of this energy and matter. [24] Similarly for a nucleon full energy E n M n c 2, where c 2.9979?10 8 m/s – speed of light and the characteristic speed of particles in the matter of nucleon, M n – mass of a nucleon. [23] At these levels there are many of the most stable and long-lived carriers; such as nucleons and the neutron stars containing a maximum quantity of composite particles and having a maximum density of matter and energy. [23] Electrical charge, energy, light, angular momentum, and matter are all quantized on the microscopic level. [25] Think about how, at a subatomic level, energy responds to our attention and becomes matter. [24] Matter is more “nothing” (energy) than “something” (particles). [24] The new school tells us that an atom is composed 99.99999% by energy and just.00001% percent by matter. [24]

The energy levels and electron wavefunctions that correspond to different states within a hydrogen atom, although the configurations are extremely similar for all atoms. [26] The energy levels are quantized in multiples of Planck’s constant, but the sizes of the orbitals and atoms are determined by the ground-state energy and the electron’s mass. [26] Large-scale constants connecting dimensions and mass of particles, and energy density and the relaxation time of particular worlds are calculated. [23] What if an object with zero mass was traveling at the speed of light? Now the relativistic energy equation would have zero in the numerator and zero in the denominator. [27] Since the strong and electromagnetic forces work against each other, quarks and gluons can form finite-sized protons; protons and neutrons assemble into nuclei larger than the protons and neutrons combined would make; electrons, with their low mass and high zero-point energy, orbit around nuclei only at great (relative) distances. [26] It?s due to three factors that all work together: forces, the quantum properties of the particles themselves, and energy. [26] The LHC has been handily demolishing this fantastical menagerie one imaginary particle at a time, and only the fact that superstrings were intentionally concocted in the first place to exist at energy levels far beyond anything remotely measurable by humanity has kept them this side of the nothingness they were pulled from. [26] Full energy of a neutron star without taking into account the energy of rest is defined by expression E s M s C 2, where C 6.8?10 7 m/s – characteristic speed of particles of the neutron star, M s – mass of the star. [23] These particles are in a wave state (let?s remember energy represents 99.99999% of it) while they are not observed. [24]

Quantum experiments proved that electrons exist as infinite possibilities or probabilities in an invisible field of energy. [24] We now know (or have remembered) that everything is energy, and now further know that quantum theory says there are multiple possibilities–in fact, infinite possibilities. [5] If it did, it would have either undefined energy (the mathematicians answer) or infinite energy (the physicists answer). [27] Please refrain from using words like “. infinite clean energy [28]

The electric charge of the proton appears in the reactions of the weak interaction in neutron matter during beta decay and reaches a maximum when the density of zero electromagnetic energy becomes comparable to the energy density of strong gravitation. 2 Analysis of electric and magnetic polarizabilities of nucleons shows that they can be understood without invoking the idea of quarks. [23] The metallic hydrogen when not activated produces a low intensity magnetic field that catalyzes the conversion of matter into energy. [26]

They have no mass, but somehow they still transfer energy (kinetic energy, to be specific) and momentum. [27] It also says that the reason an object at rest has any energy at all is because it has mass, which is why this equation is also known as the mass-energy equivalence. [27] Just like how spring breaks when stretched too far, or when the springs are squashed so that the springs break and the two objects fuse, atoms will also break its bond when stretched too far (situation v), and will reach extremely high energy upon extreme contraction of the bond (situation i). [6]

When the metallic hydrogen is activated, its magnetic potential increases greatly and the energy produced is substantial. [26] No particle that exists is massless, if they were, they would have zero density and zero energy. [26] It holds that one energy particle can influence another energy particle, even when the particles do not touch in any way and even when they are separated by billions of miles. [5]

Oh space can also be folded like a blanket, so with enough energy “warping space” you can punch right through the folds no need to travel light years of actual distance between stars. [26] Here’s what the first six terms of the relativistic energy equation look like. [27] How on earth would anything that had no mass or energy interact with something that did? Wishful thinking? Magic? Lots of math? Folks want to pay lip service to EMC^2 all day long, and then throw it under the bus the first opportunity their convoluted mathematical modeling demands it. [26] No mass means no density or energy, which means no interaction, thus it can not be the causation of anything. [26] Ok, so the forces are at equilibrium at minimum energy stage, but I still dont understand what this negative energy means. [6] Without knowing the gradient and the zero energy reference used, it means nothing. [6]

Quantum physics discovered that physical atoms are vortices of energy that are constantly vibrating. [5] They?ll just hang out in the quantum field as pure energy waiting there, in case we do decide to focus on them. [5]

At the most fundamental level, the Universe, and everything which comprises it, is pure vibratory energy, manifesting itself in different ways. [5] PT-symmetric systems exhibit a feature that Hermitian systems cannot; the energy levels become complex when there is a change on P/T symmetry. [26]

This equation says that an object at rest has energy, which is why it is sometimes called the rest energy equation. [27] The carriers of the substance are graons, praons, nucleons, neutron stars and other similar objects with the highest energy density. [23]

There’s a different one for time (time dilation) and a different one for space (length contraction) and now there’s a different one for momentum (relativistic momentum) and another different one for energy (relativistic energy). [27] L. Rev. 1249, 1250 (2013) (suggesting that conventional accounts of consumer choice fail to account for “the time and mental energy spent” choosing between competing goods). [8]

Obviously such constant line will intersect the energy curve at two points. [6] The lowering of the energy (approximately 4.52 eV), means that the hydrogen molecule is more stable in this configuration. [6] Here is a block quote – The sounds they emit work as a type of energy medicine that has been known to heal pain and stress disorders. [5] The question must be raised about the need for the existence of dark energy. [23] In the last blog post, we explored the first principle: Everything is Energy. [5] The theory is acquiring great importance in the study of universal mechanisms of formation of objects, the emergence of fields and forces, their origin and interaction at different levels, and of matter in an infinite universe. [23]

Objects on different levels of matter generate radiation in the form of particle streams and field quanta, aggregating to form the fundamental forces acting on objects as well as other levels of matter. [23]

The history of moving deep into levels of the matter – from atoms to elementary particles down to quarks is considered. [23] Leading to an infinite nesting of levels living matter in each individual living organism. 46 As an illustration, it is known, that in the human body there is so much bacteria that their total mass may be up to two kilograms. [23] The Universe consists of an infinite number of enclosed levels of matter. [23] Categorization of cosmic objects based on the levels of matter are the stepping stones of an infinite hierarchy of cosmic systems, similar to geometric progression. [23] The detailed philosophical analysis of the theory of infinite nesting of matter was carried out by Sergey Fedosin in 2003. 45 At each level of matter, characteristic basic carriers and boundary points of measurement are allocated. [23] The theory of infinite nesting of matter is justified by the law of similarity of carriers of different scale levels. [23] Nesting is defined that an organ is composed of many cells, and the body – of many organs, etc. In addition to such qualitative conclusions, in the theory of infinite nesting with the help of similarity of matter levels can determine some quantitative regularities. [23] The idea of infinite nesting of matter was the basis for the construction of substantial electron model and explaining electronic spin. [23] Infinite hierarchical nesting of matter claims the unacceptability of the general theory of relativity to describe the entire Universe, and precludes the Big Bang as a likely scenario of the Universe’s development. [23] The proposed theory Infinite Hierarchical Nesting of Matter is a cosmological framework that suggests that matter can be divided or reduced infinitely, as opposed to atomism. [23] The physical theories and infinite hierarchical nesting of matter. [23]

In the substantial neutron model and substantial proton model it is found that the mass of the nucleons is in a narrow range of masses as a consequence of the equation of state of hadronic matter and its evolution in the field of strong gravitation. [23] The general field is universal in the sense that it operates at all levels of matter and allows us to describe the equation of motion of any object with the help of one tensor equation. [23] In this case there is an interpenetration of the living and nonliving matter, and a clear correlation between the size and mass of living carriers and the corresponding values of physical objects at different levels of matter. [23]

At the quantum level, a particle in this upside-down potential is in a bound state strongly localized at the origin. [26] Others particles with large escape velocity, remain dispersed in space and serve as material for a variety of potential fields. [23]

In each particle, no matter how small it is, “there are the cities occupied by people, cultivated fields, and the sun, the moon and other stars like ours” – claimed the Greek philosopher Anaxagoras in his work on gomeomeriya in V century BC. [23] Solids, like the other states of matter, can be classified according to whether their fundamental molecular units are atoms, electrically-neutral molecules, or ions. [7] Particles combine to form atoms, atoms then combine to form molecules, and these molecules are the origin of visible matter. [5] Therefore, Oldershaw introduces for the electron, a concept of a halo consisting of tiny particles that form the matter of the electron. [23] Matter is quantized because it is composed of individual particles that cannot be subdivided; it is not possible to have half an electron. [25] This cosmological paradigm completely abolished the formal restrictions of atomism in the theoretical and experimental study of the levels of matter such as elementary particles. [23] The main scales in this range of levels of matter are the level of elementary particles and the level of stars. [23] What distinguishes solids, liquids, and gases- the three major states of matter — from each other? Let us begin at the microscopic level, by reviewing what we know about gases, the simplest state in which matter can exist. [7] Is there a somewhat more elaborate theory that can predict the behavior of the other two principal states of matter, liquids and solids? Very simply, the answer is “no”; despite much effort, no one has yet been able to derive a general equation of state for condensed states of matter. [7] In condensed matter, these interactions dominate, and they tend to be unique to each particular substance, so there is no such thing as a genrally useful equation of state of liquids and solids. [7] One important thing to know about ions is that in ordinary matter, whether in the solid, liquid, or gaseous state, any positive ions must be accompanied by a compensating number of negative ions. [7] The three states of matter are not simply three points on a continuum; when an ordinary solid melts, it usually does so at a definite temperature, without apparently passing through any states that are intermediate between a solid and a liquid. [7] Even the most casual inspection of the above table shows that solids and liquids possess an important commonality that distinguishes them from gases: in solids and liquids, the molecules are in contact with their neighbors. gAs a consequence, these condensed states of matter generally possess much higher densities than gases. [7] There is a difference between the concepts of “quantity of matter” and gravitational mass, implying that under certain conditions, different amount of substance may possess the same gravitational properties. [23]

Nesting of living matter in natural systems manifests as the distribution of organisms of different species scale or levels according to mass and size. [23] This substance is a multicomponent structure consisting of the objects of basic levels of matter, which appear to be the most dense and stable due to the balance of the corresponding fundamental forces. [23] The distribution of material objects in the Universe is described with the help of scale dimension, which extends over all levels of matter. [23] Sukhonos highlights the fractal phenomena in nature, and also proves bimodality when objects show supplementary properties: spiral and elliptic galaxies; subdwarfs as primary stars of the Galaxy with deficiency of heavy elements, and usual stars of the main sequence; planets external and internal; processes of synthesis and division, monocentric and polycentric structures at different levels of matter. [23] It allows the observer to compare attitudes of similarity between various levels of matter and by that in advance to predict still more about investigated badly objects. [23] Due to the similarity of matter levels, each basic level of matter consists of the objects of the underlying basic level of matter. [23] This is how the principle of nesting of matter is realized and the substance is found that the material objects at all levels of matter are built of. [23] Transitions from one level of matter to another are carried out under the law of transition of quantity and in quality when the quantity of carriers in object exceeds the admissible borders of the measurements typical for the given object. [23] According to his work, matter is concentrated to the given levels, basically in the form of nucleons and stars, and stars also in the majority are a part of galaxies. 32 33 Oldershaw remarks, that the overwhelming quantity of matter in space contains in the lightest elements – hydrogen and helium, and at the level of stars – in dwarf stars with masses ranging between 0.1 – 0.8 solar masses. [23] The study of the origin of fundamental gravitational and electromagnetic interactions in articles 5 3 leads to the following picture of disposition of the basic levels of matter: the level of graons – the level of praons – the level of nucleons – the level of stars – the level of supermetagalaxies. [23] Subsidiaries of inert matter arise from elementary particles of the parent structure by their gravitational condensation in accordance with the theory of Jeans. [23] Matter doesn?t need to be made of finite-sized particles to wind up creating the macroscopic Universe we know and love. [26] In condensed matter physics a notable example is ferromagnetism; in particle physics the best known example is the Higgs mechanism in the standard model. [26]

By calculation it then follows, that processes at the level of nucleon matter proceed in ? time more quickly, than at the level of neutron stars. [23] These parallel analogues from different Scales have strongly analogous morphologies, kinematics and dynamics. 1 From a purely physical point of view these similar relations lead to similarity of matter levels and SP? symmetry, which asserts the invariance of physical laws operating on different levels of matter. [23] As a consequence, SP? symmetry similarity is generated between the basic levels of matter. [23] Each level of the matter includes carriers with a specific spectrum of sizes and masses. [23] Metagalaxies, nucleons, and maximons belong to the basic levels of matter. [23] Eighteen levels of matter from preons up to metagalaxies were divided into basic and intermediate stages in masses and dimensions, and between them can be derived relations of similarity. [23] Examples of fractal structures at various spatial levels of matter are the result. [23] The matter that we experience with our senses is far removed from this level. [7]

Irish scientist Edmund Edward Fournier D’Albe has made the assumption, that the scale of ranks reaches also into matter, by reduction. 10 According to Fournier D’Albe, a denominator of a progression, i. ?. the attitude of the linear sizes of a star and atom or the sizes of a star, of supraworld and stars of “our” world, the atom of supraworld, is expressed by number 10 22. [23] It is this extreme contrast with the gaseous states that leads to the appellation ” condensed states of matter ” for liquids and solids. [7] Gases at very high pressures can have densities that exceed those of other solid and liquid substances, so density alone is not a sufficiently comprehensive criterion for distinguishing between the gaseous and condensed states of matter. [7] Other physical properties, such as the compressibility, surface tension, and viscosity, are somewhat more useful for distinguishing between the different states of matter. [7] Rather than try to develop a strict scheme for classifying the three states of matter, it will be more useful to simply present a few generalizations. [7] Liquids and solids share most of the properties of having their molecular units in direct contact as discussed in the previous section on condensed states of matter. [7] A basic law of nature, the electroneutrality principle, states that bulk matter cannot acquire more than a trifling (and chemically insignificant) net electric charge. [7] State the major feature that characterizes a condensed state of matter. [7] Describe some of the major observable properties that distinguish gases, liquid and solids, and state their relative magnitudes in these three states of matter. [7]

In addition to the widely used four-dimensional space-time construct, the theory of infinite nesting of matter claims the existence of a fifth, scale dimension. [23] Ann. 49)); W.T. Rogers Co. v. Keene, 778 F.2d 334, 339 (7th Cir. 1985) (noting that “useable” trademarks are “for all practical purposes infinite”); William M. Landes & Richard A. Posner, Trademark Law: An Economic Perspective, 30 J.L. & Econ. 265, 274 (1987) (” ords that will serve as a suitable trademark are as a practical matter infinite.”). [8]

To be sure, the claim that potential trademarks, broadly defined, are inexhaustible is tautologically true: there are infinite combinations of letters and other symbols — including sounds and colors — any of which might serve as a mark. 2 × 2. [8] The most famous physicist since Einstein (Hawking) claimed that everything in the universe came out of an original singularity of “zero volume and infinite mass density.” (Also erroneously applied to black holes.) [26] In a nutshell, this means there were once infinite possibilities, but by observing, the observer collapsed that reality into one perceivable reality, or, into one perceivable particle. [5] In addition to infinite nesting of physical material objects of different levels, an infinite nesting of life is found – inside the autonomous living organisms from one level: the smallest prions and ending with the whales are present in all other living structures of lower levels of scale. [23] It is found that, despite the infinite number of particular worlds, all the basic parameters of the Universe are finite. [23] “The Universe, hence, not only is spatially infinite, but also structurally diverse, as its structure includes space systems of different orders and the sizes.” [23] According to which, the Universe represents an infinite set of systems escalating in order of complexity then entering each other. [23] That in an infinite Universe the photometric paradox is eliminated. [23] Baruch Spinoza was an adherent of the Infinite hierarchical model of the Universe. [23]

Although the expansion generates an infinite number of terms, only the first n + 1 of them are non-zero. [27] In some cases where the trademark is well-known, the “choice of a confusingly similar mark, out of the infinite number of marks in the world, itself supports an inference bad faith.” 11 × 11. [8] Interestingly, the ? symbol means both undefined and infinite. [27]

Of course, just as for utility patent law, this potential innovation benefit does not mean that trademark rights should be expanded without bounds — benefits for first movers have costs, such as impeding follow-on innovations by second movers. [8] You were wondering about the Coulomb potential (the equation you provided). [6] Even though the real numbers are embedded in the complex numbers, we cannot say that one complex number is greater than another complex number, so it makes no sense to say that the “bottom” of the potential is at x0! One must think in new ways when working in the complex domain. [26] When the fuel is activated by a high potential EMF field the LENR reaction produced by the metallic hydrogen increases exponentially. [26]

For a rough turning points in a quantum harmonic oscillator, or beyond the well edges in a finite potential well. comparison, you calculate the ground-state energy of a proton 48. (a) Use Equation 35.8 to draw an energy-level diagram for the first six energy levels of a particle in a cubical box, in terms of confined to 1-fm-diameter atomic nucleus and that of an electron h2/8mL2, and (b) give the degeneracy of each. confined to a 0.1-nm-diameter atom. [10] In general, these exponentials drop very rapidly across the barrier width unless the particle energy E is close to the barrier energy or the FIGURE 35.12 A potential barrier of height U, particle mass m is small. [10]

The lower-energy states in a covalently bound diatomic molecule Answers to Chapter Questions 679 can be found approximately from the so-called Morse potential U1r2 5 U01e21r2r02/a 2 e221r2r02/a2, where r is the atomic separa- and PV cells? semiconductor band-gap energy. [10] My text book states that Mechanical energy is the sum of K (kinetic energy) and U (potential enery), while the definition of mechanical energy states that mechanical energy is energy that depends on the position OR motion of the masses. [9] At the top the energy is all potential, mgh, and at the bottom all kinetic, ½ mv 2 + I 2, translational plus rotational. [9] Find the ground-state energy for a particle in a harmonic oscillator potential whose classical angular frequency v is 1.031017 s21. ing the sides of a box different lengths remove the degeneracy 24. [10]

A particle in an infinite square well makes a transition from a is also a solution, where a and b are arbitrary constants. higher to a lower energy state; the corresponding energy decrease is 33 times the ground-state energy. [10] The ground-state energy for an electron in infinite square well A 2 “2 a ‘ 2c 1 ‘ 2c ‘ 2c 1 U1x, y, z2c 5 Ec is equal to the energy of the first excited state for an electron in 2m ‘x2 ‘y2 1 ‘z2 b well B. How do the wells? widths compare? 37. [10]

What?s the quantum number for a particle in an infinite square well if the particle?s energy is 25 times the ground-state energy? 31. [10]

Kinetic Energy and Work (W AK) Question: A skier of mass 65.0 kg is on an incline of 15.0 degrees, and has an initial velocity down the incline of 5.00 m/s. [25] Kinetic Energy and Work (W – AK) EC Question: A 15.0 kg crate having an initial horizontal velocity of 5.00 m/s, is pulled by a force of 50.0 N at an angle of 20.0 degrees above the horizontal, a distance of 90.0 m o. [25]

The thermal kinetic energy that the individual molecular units do have at temperatures below their melting points allows them to oscillate around a fixed center whose location is determined by the balance between local forces of attraction and repulsion due to neighboring units, but only very rarely will a molecule jump out of the fixed space alloted to it in the lattice. [7] The energy added to an object to take it from an initial speed of zero to a final speed of something is its kinetic energy. [27]

In the lower curve above, imagine you put a particle with negative constant total energy, graphically it will be a constant curve at some negative value but is still more positive than the global minimum. [6]

Ions, you will recall, are atoms or molecules that have one or more electrons missing (positive ions) or in excess (negative ions), and therefor possess an electric charge. [7]

Time is also denoted as an independent coordinate from space, which also is a derivative of velocity and development of matter. [23] Matter is organized in stable conditions and are under the influence of fundamental forces and interactions with objects of different systems. [23] To the question on similarity of atomic and galactic structures of matter, in Russian. [23] Turtles_all_the_way_down – Indirectly concerns to the questions on boundless division of the matter and occurrence of the world, by analogy. [23]

Because time travel is considered to be unphysical, tachyons are believed by physicists either not to exist, or else to be incapable of interacting with normal matter. [26] The Universe is eternal, thus carriers of matter are constantly born and are then transformed into carriers of similar and disparate scales. [23] A system of the Universe was published in the book “Rise of the Worlds” (2003). 52 The system covers Genesis of inert and living matter. [23]

The Pauli Exclusion Principle goes a long way towards explaining why matter occupies space. [26] Delocalization, plus the Pauli Exclusion Principle explains how matter makes space. [26]

The first term is the classical equation for kinetic energy. [27] Using the work kinetic energy method, draw a sketch and cal. [25]

If the rest mass m is Complex this implies that the denominator is Complex because the total energy is observable and thus must be real. [26]

The photon energy is just high enough to raise an electron mass m in this well, giving separate expressions for even and odd to its first excited state. [10] Regarding the rest of your question, when an electron drops to a lower orbit the mass of the atom decreases by exactly the right amount to supply the energy to the photon. [9] FOLLOWUP QUESTION: In a previous answer you stated the mass of an electron decreases as it shifts to a lower orbit and releases a quantum (hf) of energy. [9] The answer is, yes and in fact nuclear physicists and particle physicists usually specify the mass of a particle by specifying its rest mass energy ( mc 2 ); for example, the “mass” of an electron is 511 keV (keV is kilo electron volt, a unit of energy). [9] ANSWER: A virtual photon (the emission of which violates energy conservation) may exist only for a very short time after which it must be reabsorbed by the original electron or absorbed by another charged particle. [9] Does quantum tunneling violate energy conservation? Explain. cited state is 1.13 eV, is the particle an electron or a proton? 3. [10] No matter what its energy a particle is bound in such a well; it can?t escape to large distances. [10] QUESTION: According to Albert Einstein’s equation “EMC2”, If you accelerate an object at twice the speed of light, will it become energy? And does it matter what type of physical composition the object has? The last question I ask. [9] It is certainly true that, given our current understanding of physical laws, experimental astronomical data suggest that there is much more matter in the universe than we observe directly as normal mass (dark matter?) and that the universe is expanding at an increaseing rate (dark energy?), but we do not really understand why these things are happening. [9] Be sure to note that my answer is qualified by “as best we know”; there are indications that maybe we do not understand gravity as well as we think we do; examples of this are so-called dark matter and dark energy, both of which are really totally puzzling to scientists. [9] Find (a) the principal quantum matter? number and (b) the energy. [10]

FIGURE 37.12 (a) Energy levels of the 1s and 2s states as a pair of atoms are brought close together. (b) With five atoms, each level splits into a group of five closely spaced levels. (c) In a crystalline solid, the large number of atoms results in essentially continuous energy bands, separated by gaps. [10] An atom has many allowed energy levels and when it is in an excited state it will fall down to its lowest state and spit out a photon. [9] For visible light the source is typically an atom which essentially behaves like an antenna when emitting a photon; here the atom drops from an excited state to a lower state, thereby providing the energy to the photon, but this does not impel it to move since it must move by its very nature. [9] A molecule has additional discrete energy states, which may be excited by particle or photon collisions. [29] In many cases, equations of a fluid type may be derived from the kinetic equations; they express the conservation of mass, momentum, and energy per unit volume, with one such set of equations for each particle type. [29] It is possible at high energies, like those generated at the Large Hadron Collider in Switzerland, to end up with a different number of particles than you started with, because the famous equation emc2 allows mass to be created from energy when the energy is extremely large. [30] Emc 2 is the energy of a particle of mass m at rest; a photon is never at rest and therefore this equation is not applicable to it. [9] DEVELOP Spectral lines result from photons emitted as a molecule where we approximated the hydrogen mass, m, with the proton mass drops from one of the energy levels of Equation 37.2 to the next lower listed inside the front cover. level. [10] At this level we can?t solve the Schringer equation for these many-particle systems, but we?ve argued–using energy and angular momentum quantiza- tion and the exclusion principle–that quantum effects are important in molecules and solids. [10] The _ quantum number (n) specifies the primary energy level of an electron and its average distance from the nucleus. [12] A principal quantum number of 7 would indicate that the _ energy level of an electron and the average distance from the nucleus were the highest. [12] How many electrons can be excited if the quantum numbers. (b) Find the corresponding energy levels. beam shines for 10 ms? 40. [10] Electron energies in a quantum wire are quan- with the energy of the upper level, in the limit of large quantum tized and so, therefore, are electrical properties such as resistivity. number n. [10] Determine the principal and orbital quantum numbers for a hy- drogen atom whose electron has energy ?0.850 eV and orbital cal elements? angular momentum L 5 112″. [10] Bands lower than 3s aren?t shown; they correspond to inner electrons, We can determine which of the allowed energy levels of a solid will be occupied in the whose levels aren?t split significantly. same way we established the electronic structure of atoms: by placing a given total num- ber of electrons in the lowest possible levels consistent with the exclusion principle. [10] Electrons are spin-12 particles or fermions; z Spin-orbit coupling results in fine-structure splitting of atomic- the component of their spin angular mo- energy levels. mentum on a given axis is 612 “. [10] Note that the high-energy band containing electrons–here the 3s/3p band–is not com- FIGURE 37.14 Band structure of metallic sodium, pletely full, meaning that energy levels in the upper portion of the band aren?t occupied by with gray indicating filled states and color electrons. unfilled states. [10] At T 5 0, states At T. 0. below EF are full. thermal energy promotes. and states a few electrons above EF are to levels above EF. empty. [10] When the atoms are far apart, they?re described by identical wave functions and associated energy-level diagrams; a given electron state, for example, has exactly the same energy in each atom. [10] A convenient unit for measuring temperature in the study of plasmas is the electron volt (eV), which is the energy gained by an electron in vacuum when it is accelerated across one volt of electric potential. [29] Electrons. and holes diffuse Electron energy Potential Conduction diffuse into into N region. [10] They are building a tokamak, a donut-shaped, man-made, artificial star that has the potential to bring the universe down to earth and provide millions of years of clean energy. [31]

The momentum may be written for a particle of mass m and speed v as p mv / where c is the speed of light; it may also be written in terms of the energy E of the particle as p / c. [9] Emc 2 means that the energy of an object at rest is its rest mass times the speed of light squared, but light is never at rest so you cannot use this formula to find its energy. [9] QUESTION: we know that mass is a state of energy, but can energy exist without mass? I mean energy itself, not the energy being transferred. [9] Continuum E U0 Quantized bound states represent particles with energy lower than the well height. [10] Particles in these unbound states can have any energy n53 whatsoever as long as it exceeds the well height; unbound energies aren?t quantized. [10] The first E112, E121, E211 E211 excited state of a particle confined to a cubical box is threefold degenerate, meaning E121 there are three distinct states with the same energy. [10] ANSWER: There are lots of ways you can come up with Bohr’s postulate, but when one first proposes a radical idea like this one the choice of constant is often empirical, that is you choose a constant which gives the right answers, in this case the energy levels of the hydrogen atom, the wavelengths of the spectrum. [9] As in (a) the ground state and (b) the first excited atoms, differences among molecular energy levels are associated with different electronic state of hydrogen. Nuclei are farther apart configurations (Fig. 37.6). [10] FIGURE 37.16 Density of states given by Equation 37.5, with shaded region indicating occu- pied energy levels. (a) T 5 0; (b) T. 0. [10] Find levels. (a) the energy and (b) the wavelength of a photon emitted in a tran- sition between the n 5 1, l 5 1 state and the n 5 0, l 5 2 state. 21. [10] A quantum harmonic oscillator emits or absorbs photons as it makes transitions among n51 adjacent levels, and the even spacing means that all transitions between adjacent levels of a pure harmonic oscillator involve photons of the same energy. -4 -3 -2 -1 0 1 2 3 4 (b) A classical harmonic oscillator moves slowest near its turning points, so it?s most likely to be found at the extremes of its motion. [10] An electron E1 E1 spontaneously jumps from a higher to a lower energy level and a photon is emitted; this (b) E2 is spontaneous emission (Fig. 36.18b). [10] Find (a) the energy and (b) the magnitude of the orbital angular momentum for an electron in the 5d state of hydrogen. they differ by only one unit of nuclear charge. [10] In BCS theory, superconductivity results from a quantum-mechanical pairing of elec- trons that leads to a lower-energy state in which electron pairs move through the crystal lattice with no energy loss to the ions, resulting in zero electrical resistance. [10] FIGURE 37.2 Potential-energy curve for Na1 FIGURE 37.3 A sodium chloride and Cl2 ions, with zero energy corresponding crystal is a regular array of sodium to infinite separation of neutral Na and Cl and chlorine atoms, bound by the atoms. electrostatic force. [10] ANSWER: First of all, electrons do not have infinite energy. [9] Determine the ground-state energy for an electron in an infinite square well of width 10.0 nm. 33. [10] Suppose you put five electrons into an infinite square well of ergies emitted in these transitions. width L. Find an expression for the minimum energy of this sys- 64. [10] A quantum harmonic oscillator has ground-state energy 0.14 eV. tures of infinite and finite square wells? What would be the system?s classical oscillation frequency f ? 6. [10] Find the width of an infinite square well in which a proton?s min- wavelength of the photon emitted. imum energy is 100 eV. 34. [10] Usually physicists show their students that the energy required to accelerate an object to c is infinite. [9] The notion that we can have infinite supplies of energy through some technological breakthrough (always in our future. ) to address the dilemmas billions of humans face on this planet is little more than wishful thinking and techno-narcissism. [31]

The probability that a particle will be found on the far side of the showing the wave function for a particle inci- barrier is therefore very low when the mass m is large, so quantum tunneling is a micro- dent from the left with energy E lower than the scopic phenomenon (Fig. 35.13). barrier energy U. It looks as if tunneling violates energy conservation. [10] Answer to Chapter Opening Question Quantum tunneling, the ability of particles to penetrate a barrier that classical physics says they don?t have sufficient energy to overcome. [10] QUESTION: Can a particle accelerator create more energy than is needed to operate it? youir answer is very much appreciated. [9] QUESTION: Regarding the de Broglie wavelength and simple model of a particle bouncing back and forth in a closed box (and no force field therein), I am trying to understand where the energy comes from if I do the following conceptual experiment. [9] QUESTION: In isotope decays and nuclear reactions, many sources give the energy of the products (neutrons, alpha particles etc.) in MeV. I understand that MeV is a measurement of energy (and has a standard conversion factor to joules) but I don’t understand how to calculate the speed/momentum of the out-going particle from this, or the recoil force on the reactants. [9] What?s the probability that the detector will find 0 a particle in the ground state of the square well if the detector is centered on (a) the midpoint of the well and (b) a point one- equation, where a2 5 mv/” and the energy is given by Equation fourth of the way across the well? 46. [10] Passage Problems 61. (a) Verify Equation 36.8 by considering a single-electron atom with nuclear charge Ze instead of e. (b) Calculate the ionization With sufficient energy, it?s possible to eject an electron from an inner energies for single-electron versions of helium, oxygen, lead, and atomic orbital. [10] The mass of a hydrogen atom is less than the mass of a proton plus the mass of an electron because of the binding energy; since it takes energy to pull the atom apart, it must have less mass than the sum of its parts. [9] The temperatures required for self-ionization thus range from 2.5 to 8 electron volts, since such values are typical of the energy needed to remove one electron from an atom or molecule. [29] Because of their small energy loss in elastic collisions, electrons can be raised to much higher temperatures than other particles. [29] You?re asked to specify the 36.3 and Example 36.1 to calculate the average radial distance rav maximum number of electrons in the device before the total elec- for an electron in the ground state. (Note: Because the probability- tron energy exceeds 25 eV. Your answer? density curve isn?t symmetric, the average radial distance isn?t 49. [10] Your answer? to an atomic electron initially in the 6d state without changing its principal quantum number? What would be the new state? Energy (eV above common ground state) 22 E2 56. [10]

The number of states available to the electrons, per unit energy interval, turns out to increase with energy. [10] For hydrogen, fine-structure splitting of the 2p state is only about gives gS 5 2 for the g-factor associated with electron spin. 50 ?eV. What percentage is this difference of the photon energy 68. [10] A higher-energy electron will then drop into the unoc- uranium. cupied state, emitting a photon with energy equal to the difference be- 62. [10] E1 E1 In 1917 Einstein recognized a third possibility: Excited atoms can be stimulated to drop (c) into lower energy states by the mere presence of a photon, again of energy appropriate to the transition. [10] Usually it is an atom, changing from an excited electronic state to a lower state, which emits light and the photon’s energy is supplied by the excess energy of the atom. [9] Laser light can be made extremely intense, since stimulated emis- spontaneous emission to the metastable state, where they?re “stuck” by the lack of sion extracts energy from many atoms simultaneously. [10] When light enters a medium, it will be absorbed only if there are electronic levels in the atoms and molecules which can receive the energy of the light. [9] Like any FIGURE 37.6 Electron probability densities for quantum-mechanical bound system, the energy levels of a molecule are quantized. [10] Molecular energy levels are therefore at the heart of today?s most global state of a diatomic molecule; also shown are environmental concern. four of the infinitely many rotational states for each n. [10] The energy of that state is higher than that of an H2 molecule and a distant H atom; for this reason H3 isn?t a stable molecule. [10] Molecules are more complex than atoms, and molecular in the excited state. energy can take additional forms. [10]

The energy it carries, of course, does not disappear but is absorbed by the matter by exciting the atoms. [9] June 7, 2018 – Dark matter and dark energy may have driven inflation, the exponential expansion of the Universe moments after the Big Bang. [30] It is thought that dark energy, not dark matter, is the origin of the acceleration observed for distant galaxies. [9] I am similarly not very sympathetic with the current use of the terms dark matter and dark energy as being some kind of statements of experimental facts since nobody has any idea what they are. [9] Why? Because everything is energy and energy creates vibrations which form matter. [32]

That?s because the exclusion princi- ple requires extra neutrons to go into higher energy states, making individual particles more likely to escape the nucleus. [10] For particle 2 at rest, the equations resulting from applying momentum and energy conservation are v 1 u ( m 1 – m 2 )/( m 1 + m 2 ) and v 2 2 m 1 u /( m 1 + m 2 ) where u is the speed of approach of m 1. [9] Explain qualitatively why a particle confined to a finite region sible energy corresponded to a speed of 1.0 m/s? cannot have zero energy. 19. [10] At the LHC things go the other way: particles with very high energies are smashed into each other to create new particles, energy is turned to mass rather than mass to energy. [9] ANSWER: What makes you think that having a mass is a prerequisite to having energy? If you accept the conservation of energy, then when an atom decays it loses energy (its mass actually becomes slightly less). [9] ANSWER: There is no way to know since the energy of the x-rays depends on the target material used, not the energy of the electron beam used to excite the atoms. [9] ANSWER: When light encounters a substance, it changes its speed (slows down) and loses energy because of its interactions with primarily the electrons in the material. [9] If you have an electron and a positron (the electron’s antiparticle), they will annihilate each other and energy in the form of photons (light, basically) will appear and have exactly the energy of the masses times c 2. [9] A material whose band gap corre- sponds to visible-light photons can absorb light energy, promoting electrons to the conduc- tion band and driving current through an external circuit. [10] It doesn’t even hold for the creation of energy since the photon is not created by annilating mass, but rather by an electron shifting orbit. [9] The question of whether a photon has mass because it has energy is addressed in an earlier answer. [9] Three 0.4 gram bbs (total mass of 1.2 grams) at 273 ft/s has an energy of 44,717, nearly 5 times as much energy. (You made a mistake somewhere since you later in your question refer to 0.5 instead of 0.4 gram bbs, but this mass would have even more energy.) [9] QUESTION: Conversion of mass to energy (fission) has been demonstrated many times in laboratory and field tests. [9] They do not lose energy significantly differently (the faster pitch lost more speed in a shorter time so its average rate of change of speed was indeed bigger). (I used 3 inches for the diameter, 0.145 kg for the mass, and 60’6″ for the distance to the plate.) [9] I do recording for the blind and recently read a discussion regarding just what you are asking, viz. how can you say I am not doing work when I hold a box when I know energy is required to do so? The gist of the answer is that muscles exert a force by individual fibers of the muscle continually slipping and then recontracting, so for this special case the individual componenets of the total force are all contiually pulling over a distance and hence doing work. [9] One simply calculates the work done by a force and defines that to be the change in energy of the particle. [9] When developing the theory of special relativity there comes a time when we want to ask what is the energy of a particle, that is what changes when we do work on the particle. [9] Here you keep the particle in its ground state and slowly increase its energy so that you must do work on the particle. [9] Treating this as a particle in a 4 2np one-dimensional square well, find the energy difference between the ground state and the first excited state. [10] ANSWER: The frequency of a particle is its energy divided by Planck’s constant. [9] ANSWER: The energy of any particle is E where p is the linear momentum. [9]

Circular orbit: States with l values 0, 1, 2, 3, 4, 5, c are given the letter labels s, p, d, f, g, h, c. maximum L These combine with the principal quantum number n to specify both the energy and angu- lar momentum of a state. [10] In the spherically symmetric s states, it turns out that the orbital angular momentum Energy (eV) associated with the electron?s motion is zero. [10] The key here is that energy is a scalar and angular momentum is a vector so two kinetic energies cannot add to zero but two angular momenta can. [9] QUESTION: electron and photon have same energy 105ev.what is the ratio of their momentum if any.My friend asked me this question but i doubt its validty. [9] A photon could collide with an electron but energy and momentum considerations would cause almost no effect on the electron’s path. [9]

Quantum mechanically, an electron can gain energy only by jumping into a higher allowed energy level. [10] The electron can occupy any energy level (special orbits) but not halfway between two of them. [9] Spontaneous and Stimulated Transitions Before After E2 What makes an electron jump between energy levels? In an upward transition, the elec- E2 tron must absorb the appropriate amount of energy. [10] During a collision, a bound electron may be excited–that is, raised from a low to a high energy state. [29] The _ states that an electron always occupies the orbital with the lowest energy available. [12] The 3s band is only half full, as Fig. 37.14 shows, and therefore electrons near the top of the filled portion have available unoccupied states with only a little more energy. [10] White dwarf Sun When the Sun collapses some 5 billion years from now, its electrons will drop into the lowest available energy states. [10] Beyond argon 1Z 5 182, shielding effects of the inner electrons result in the 4s states having lower energy than the 3d states. [10] One or more electrons go into higher energy states, raising the overall energy and (36.2, 36.3) resulting in a repulsive interaction. [10] A smaller coil carries AC current at a frequency f corresponding to photon energy hf that would flip the spin of an isolated nucleus in the field B. The coil emits electromagnetic waves, and if the nuclei absorb the associated photons, then they flip into their higher states and drop back, emitting radiation of frequency f in the process. [10] The only massless particle we know is the photon which has an energy Ehf where h is Planck’s constant and f is the frequency. [9] QUESTION: does dark energy exist within the realms of particle physics.as the distances are as vast in the cosmos. [9] What?s the essential difference between the energy-level struc- well, what would be the minimum energy for the alpha particle? 22. [10] The energy of the electron would increase appreciably even though its speed would not. (I have always thought that high-energy accelerators are not well named since very little acceleration goes on.) [9] Paired electrons move coher- Bc Applied field ently through a superconductor without energy loss to the ion lattice, resulting Applied field in zero electrical resistance. [10] For ex- E50 ample, imposing a magnetic field on an otherwise spherically symmetric atom breaks the symmetry and may split energy levels that were previously degenerate (Fig. 35.18). [10] Note the widely qualitatively similar to that of hydrogen. However, the more complicated structure of a mul- separated 4s and 4p levels, with 3d between tielectron atom shifts some energy levels (Fig. 36.16). [10] As more and more atoms come together, initially identical energy levels split into ever more finely spaced levels (Fig. 37.12b). [10] When atoms join to make solids, individual atomic energy levels separate to form Conduction band bands. [10] An energy level usually refers to a specific allowed energy of the atom. [9] Use Fig. 36.17 to determine the energy difference between the 3p Fig. 36.17, and then subtract to get the energy difference between the states of sodium. 3p levels. [10] If an atom is in its lowest (ground) energy state, it can go no lower, that is, cannot lose any energy. [9] A group of hydrogen atoms is in the same excited state, and pho- tum component on a given axis yield? tons with at least 1.5-eV energy are required to ionize these atoms. [10] In the lowest energy state, the atoms of a solid are arranged in a regular, repeating pattern; the solid is then crystalline. [10] In a quantum- mechanical treatment of molecular energetics, we consider rotational and vibrational energy states as well as electronic configuration. [10] How could those physicists be wrong? Quite simply because the apparatus they describe is designed to have a very low (not zero, since we agree that is not possible) energy loss when the gliders collide and to have minimum friction (not frictionless as you state). [9] ANSWER: In principle he is right in the following sense: if you can take more energy from your environment than you lose via friction (heat, as you state), you can keep going forever. [9] ANSWER: Two reasons are: nuclear reactions leave the residual nuclei in excited states and gamma rays are emitted when they deexcite; and the fusion adds considerable thermal energy to the system resulting in black body radiation. [9] ANSWER: Where did you get the idea that “energy has mass”? Light has energy but does not have mass. [9] ANSWER: There is always mass energy associated with binding forces, but you cannot trace mass energy to binding. [9] ANSWER: Since the sun is radiating energy, its mass must be getting smaller. [9] The possiblity of converting electromagnetic energy into mass is addressed in another earlier answer. [9] A gamma ray, provided it has enough energy to create twice the electron mass, can create a positron-electron pair; this is called pair production. [9] Light can certainly convert into mass; the best known example is called pair production where a photon (with sufficiently high energy) turns into an electron-positron pair. [9] Since energy and mass are interchangeable I feel like light must have at least convertible mass. [9] FOLLOWUP QUESTION: A followup question if you don’t mind — just to check my numbers: If the speed of light squared is roughly 900,000,000 m/s then a 1 kilogram block of butter should yield 900,000,000 joules of energy – right? One website said that a 100 watt light bulb requires 8,640,000 joules to burn for 24 hours. [9] Suppose that a very massive object collides elastically (which means no energy is lost in the collision) with a very light object at rest; imagine a bowling ball hitting a BB. After the collision the speed of the bowling ball is almost the same as what it was when it started and the speed of the BB is almost twice the bowling ball’s initial speed. [9] ANSWER: Specific heat quantifies the amount of energy needed to increase the temperature of 1 kg of something by 1 degree C. An inifinite specific heat would mean that you add energy to the object but its temperature does not increase at all. [9] ANSWER: Because the water is very transparent to visible light, this means that very little energy is left in the water by the light passing through. [9] ANSWER: The amplitude of a light wave is usually specified by the maximum magnitude of the electric field, units of N/C (newtons per coulomb) and does not specify an energy. [9]

I recently started wondering if light wavelength, frequency and amplitude are really measurements of pulsating light particles’ detectable energy, as if the light particles are glowing or even turning off and on, rather than descriptions of the shape of a light particle’s physical path. [9] The Schringer equation gives the wave function for nonrelativistic particles and leads to energy quantization for confined particles. [10] If all sides of a cubical box are doubled, what happens to the ground-state energy of a particle in that box? Section 35.2 The Schringer Equation 10. [10]

U How likely is this phenomenon, called quantum tunneling? That depends on the rela- E tion of the particle energy E to the barrier energy U, and also on the width of the barrier. [10] These include quantized energy levels, nonzero ground-state energy, nonclassical probabilities, and agreement with classical physics at large quantum numbers. [10] The distinct energy levels are labeled by the quantum number n, called the principal quantum number. [10] As with hydrogen, an elec- tron at the nth energy level can have any of the n values l 5 0, 1, 2, c, n 2 1 for the or- bital quantum number. [10] In general, each energy level is associated with one spherically symmetric wave func- tion and a number of nonsymmetric ones. [10] Qualitatively, we still find energy levels characterized by the principal quan- tum number n. [10] The excitation process is called pumping, and the particles that don?t obey the exclusion principle, there?s no limit to the number of excitation energy source is the pump. [10] Would the amount of energy contained in a sphere (Planck length/2)^3 make that sphere larger or smaller, regardless of the fact that it remains the smallest unit measurable? If so, I can’t help but visualize the universe as a bag of marbles–each marble being a Planck sphere. most of which are less massive than the Planck particle. [9] There is something in field theory referred to as vacuum polarization ; here, particles can “pop into and out of” existence as long as they pop out quickly enough that the apparent violation of energy conservation does not violate the uncertainty principle. [9] The energy of any particle is E where p is the linear momentum. [9] The bottom line is that the increased energy the particle will have will come from whoever moves the wall and that wall cannot be moved instaneously. [9] Cosmic rays can have a broad spectrum of energies, an unpredictable location where they will hit, and an uncertainty as to what they will interact with if anything at all; accelerators put the particles where you want them, with the energy you want them to have, and on specifically what you want them to hit. [9] Much energy (more than 17 MeV) is released in the reaction which ends with a 4 He nucleus and a neutron; the reason for this big energy release is that the alpha particle is very strongly bound. [9] They found that in their model system with high energy and at small scale, the system was much more likely to return multiple particles upon sending in just one, than to come out with the initial particle and no more, which was a huge surprise. [30] A quantitative analysis shows that minimum to be such that we can no longer be x sure the particle energy is lower than the barrier energy. [10]

If you would accelerate a hydrogen atom to an energy of 100 TeV (greater than any accelerator on earth can achieve) you would increase its mass by a factor of about 100,000, so it would have a mass on the order of 10 -20 kg. [9] Historically, such a model was ruled out because an electron moving in a circle radiates its energy away and it would very quickly spiral into the center of the atom. [9] Putting the electrons outside then became imperative and Bohr invented his model of the atom by postulating certain rules for orbits which would be special in that electrons in those orbits would not radiate away energy. [9] All the outer-shell electrons have essentially the same energy; the corresponding ionization energy is high; and there?s little tendency for these electrons to interact with other atoms. [10] For atoms with unfilled inertia (10.3, 11.3) outer shells, it?s energetically favorable for electrons to pair with opposite spins; this ? Rotational energy (10.4) causes an attractive interaction. [10] When atoms from these different regions of the periodic table -2 come together, it takes relatively little energy to transfer electrons between them. [10] An electron collides with atoms and transfers some of its energy to them thereby heating up the material. [9] If the electrons were not replenished, the work function would increase so that, eventually, the photons would have insufficient energy to remove any more electrons. [9] For silicon, the band tion and U0, r0, and a are constants determined from experimen- gap is 1.14 eV; photons with less energy can?t promote electrons to the tal data. [10] Compton scattering of photons (scattering from electrons) reduces the energy of the photon and the lost energy is carried off by the electron. [9] In a PV cell, photons in- d. decrease both the fraction of solar energy absorbed and the cident on a semiconductor PN junction promote electrons to the amount of absorbed energy lost as heat. conduction band, producing electron-hole pairs and driving current through an external circuit (Fig. 37.25). [10] Horizontal lines denote two atomic is the reverse of stimulated absorption (Fig. 36.18c). energy levels, and the wave is a photon with energy equal to the difference between the Spontaneous emission, stimulated absorption, and stimulated emission play major roles two levels. (a) Stimulated absorption; (b) spon- in the transfer of radiation through gases. [10] Find an expression for the energy of a photon required for a tran- sition from the 1l 2 12th level to the lth level in a molecule with Exercises and Problems rotational inertia I. [10] Key Concepts and Equations Molecules exhibit both rotational and vibrational energy, giving rise to a rich structure of quantized energy levels and the resulting spectra. [10] Its rotational inertia energy levels. ? is then given by Equation 10.12: I 5 mR2. [10] Solv- ing the Schringer equation then leads to quantized energy levels. [10] This equation says that mass is just another form of energy and tells you how much energy a mass m contains. [9] What this equation says is that a mass M, at rest, has an energy of Mc 2. [9] Specific heat is the amount of heat needed per unit mass to raise the temperature by 1 degree C. Gases are a little different from solids or liquids in that they can appreciably expand when heated, hence losing some of the energy to work done by the expansion. [9] If you pull them apart, you have to do work, right? Hence you increase the energy of the system and therefore increase the mass. [9] In your second determination, if you put the mass at its equilibrium position (at xd ) you must do work on the system and you cannot use energy conservation; it will not go there on its own. [9] For example energy may be written as a force times a distance (this kind of energy is often called work) and force has dimensions ML/T 2, and distance is, of course, L, so together they are ML 2 /T 2. [9] Equation 36.3 is indeed a solution to the Schringer equation for hydrogen, with energy E1 5 213.6 eV. dr FIGURE 36.2 A thin shell has volume dV 5 4pr2dr; In deriving expressions for a0 and E1, we?ve shown how Schringer?s theory gives thus the probability per unit radial distance is two fundamental parameters of atomic physics: the Bohr radius and the hydrogen 4pr2 times the probability per unit volume. ground-state energy. [10] If a certain state in a system decays to the groundstate of the system in a certain time, then the energy of that state cannot be measured perfectly accurately, that is the state has an inherent width or uncertainty. [9] If not, why not? the energy separation between adjacent quantum states. 8. [10] Within just a few years, though, partly motivated by the success of this model, a new branch of physics, quantum mechanics, was developed which provides an accurate picture of both how we should think about atomic structure and why certain atomic states do not radiate away their energy. [9] Cubical Rectangular Two or more quantum states with the same energy are termed degenerate. [10] INTERPRET We?re asked about the energy difference between two EVALUATE We have atomic states (3p1/2 and 3p3/2), and we?re given the wavelengths of photons emitted in transitions from those states to a common end state hc hc 5 3.42310222 J. 13s2. [10] We know that those photons carry off energy equal to the differ- DE3p 5 588.995 nm 2 588.592 nm ence between the energies of the starting and ending states. [10] Photons with energy lower than a semiconductor?s band gap states. [10] It absorbs a photon of energy 0.19653 eV and jumps to the aren?t readily absorbed by the material, so a measurement of ab- n 5 1, l 5 1 state. [10] Applying electro- magnetic radiation with the appropriate photon energy will flip nuclei into the higher energy state. [10] Putting nuclei in an external magnetic field creates two possible energy states, as suggested in Fig. 38.4a, depending on whether the nuclear magnetic mo- ments are more nearly parallel or antiparallel to the field. [10] If we solve the Schringer equa- spread in the turning points reflects the higher tion for this potential-energy curve, however, we find oscillatory solutions on either side energy of the higher-n states. of the barrier, joined according to the continuity conditions on c and dc/dx by exponen- tial functions within the barrier. [10] At typical temperatures, only the ground and first vibrational levels are significantly populated, but with energy distributed n0 l3 among many rotational levels. [10] Mak- Energy, E E111 E111 ing the sides different would remove the degeneracy, splitting a single energy level into Light intensitythree (Fig. 35.17). [10] The energy from the light gets converted into mass via Emc 2, but that amount of mass is extraordinarily tiny, way smaller than you would be able to measure. [9] The reason is that a higher percentage of mass is converted to energy in fusion because of the differences in binding energies of very light and very heavy nuclei. [9] The energy which the photons carry away from the flashlight get their energy from chemical reactions in the batteries and these chemical reactions result in a loss of mass. [9] Normally, the classic example of electron-positron annihilation results in annihilation resulting in two photons (or rarely, more than two photons) because the mass energy available is not large enough to create anything else. [9] There are ways to make energy from quantities other than mass and velocity. [9] The energy of a large mass is given to a small mass and therefore the large velocity. [9] The reason we think of fission as a great source of energy is that this tiny amount of energy is a very large fraction of the mass energy of the fuel, on the order of 1%, huge compared with more conventional energy sources like burning coal. [9] “significant” is like only 1% of the original mass, so if the mass of the nucleus is say 5×10 -25 kg then the energy released by its fission would be about mc 2 (5×10 -25 )(3×10 8 ) 2 /1004.5×10 -10 J. To put this into perspective, 1 J is approximately the amount of energy required to lift 1 kg to a height of 10 cm. [9] And, yes, if the energy is decreasing, so is the total mass. [9] What this means is that a significant fraction of the mass energy is converted into heat (and other) energy. [9] ANSWER: You are asking two questions; if a 95 mph ball loses energy faster than a 90 mph fastball (it does) you cannot conclude that it “is faster” (by which you mean, I presume, when it passes over the plate). [9] ANSWER: An electron does not “use” energy to rotate around the nucleus any more than the moon uses energy to rotate around the earth. [9] ANSWER: The energy released in a single fission event is on the order of millions of electron volts (MeV) and 1 MeV1.6 x 10 -13 Joules. [9] ANSWER: Not every photoelectric event is exactly at the surface and the electrons lose energy getting to the surface. [9] ANSWER: It is really not possible to convert an isolated atom completely to energy. [9] In a material, the energy could be transferred to the atoms of the material and then the “stopping” is simply a disappearance of the light. [9] Recently physicists have successfully stopped light (in a very ultracold cloud of atoms) and then been able to “restart” it, but this is done by storing the energy and information in the atoms and then cleverly retrieving them. [9] QUESTION: When we split an atom we can produce a nuclear reaction, which can be destructive in the case of a bomb or constructive in the case of energy production. [9] QUESTION: I was wondering about the ubiquitousness of Planck’s constant in energy equations. [9] Determine the constant n in Equation 37.4 for potassium chloride perature would the thermal energy kT be sufficient to set di- (KCl), which has the same crystal structure as NaCl and for atomic oxygen into rotation? Would you ever find diatomic which r0 5 0.315 nm and U0 5 27.21 eV. oxygen exhibiting the specific heat of a monatomic gas at normal 44. [10] He and Deffner chose to test, using new equations they developed, whether one specific quantum field theory held true in the rare case of a system of extremely small size and extremely high energy — and it did. [30] Electric fields of reasonable magnitude can?t provide this energy, so the electrons are stuck in the filled bands. [10] Because nuclei also experience magnetic fields from the electrons moving around them, the exact energy required is extremely sen- sitive to the details of the electron distribution–that is, to the surrounding molecular structure. [10] If you are interested in Compton scattering from a very high energy electron beam from an accelerator, then you would have to work out the kinematics for a moving electron. [9] An electron will emit energy if it is accelerated which is how a radio antenna works. [9] Like well-choreographed dancers, the electrons all move together in a way that precludes energy loss to the ion lattice. [10] The recombination is not possible with a single electron and a single proton because energy and momentum conservation cannot be obeyed. [9] FIGURE 36.6 Classical electron orbits with the Space Quantization same energy but different angular momenta. [10] QUESTION: if you had two balls of opposite polarity i.e. a negative and a positive ball, could they come together and stay together if they were incapable of giving up any energy to the surrounding space. [9] QUESTION: When energy is used to do work like move something or break something, is all the energy still conserved in another form or is some of it used up in the work? If, for example, you hit a concrete block with a hammer and shatter it, where does the energy from the blow end up. [9] QUESTION: Based on Physics, is a 90 MPH Fastball Slower or Faster than a 95 MPH. At work we are trying to determine if the 95 MPH fastball loses energy faster than a 90 MPH fastball. [9]

I have done no work on the system which would have provided the additional energy, and I don’t need to determine the particle’s position-velocity uncertainty profile at any time point. [9] ANSWER: In a recent New York Times Op-Ed piece by Brian Green he points out that the earth is being constantly bombarded by cosmic rays with far more energy than available at the LHC, and no black holes have caused any damage during the several billion years the earth has been here. [9] You asked for the answer in watts, but a watt is not a unit of energy, it is a unit of power; power is the rate of using energy. (Notice some time that the units used for energy consumed on your electric bill is the kilowatt-hour, since power times time equals energy.) [9] What do you think of the possibility that dark energy is also diffused throughout higher dimensions, thus explaining why it appears weaker than it should be in our 3D universe? (If necessary I could look up the exact ratios of gravity to strong, weak, and electromagnetic force and I could look up some similar stats on dark energy predictions vs observations but I don’t think this is necessary to answer my question.) [9] ANSWER: The energy of a photon is not determnied by its speed but by its frequency. [9] ANSWER: The photon has a different energy in the moving frame and therefore a different frequency. [9] ANSWER: A photon may decrease its energy (increase its wavelength) by colliding with something. [9] ASSESS Our answer is about 2 meV, much lower than the eV-range DEVELOP The quantization condition E 5 hf relates photon energy and frequency; since fl 5 c, we also have E 5 hc/l. [10] Show that the wave- Section 37.2 Molecular Energy Levels length of the emitted photon is l 5 4p2Ic/hl. [10] And, if there is an inelastic collision between two atoms, one or both become excited and then they deexcite by radiating photons which have the energy lost initially in the collision; energy is always conserved in an isolated system. [9] If I have a cup of hot tea sitting on a table in the cool morning air, the jiggling atoms and molecules in the tea will bang into the relatively less jiggling atoms and molecules of the air, and impart the thermal energy into them, until thermal equilibrium is reached between the tea and the air. [9] A gas of HCl molecules shows spectral lines that result from transi- EVALUATE (a) The energy difference D1DE2 between adjacent transi- tions between pairs of adjacent rotational energy levels. [10] ANSWER: The average energy of a molecule is proportional to the temperature. [9] The average energy per molecule will remain constant because that is what temperature measures. [9] The temperature of something is a measure of how much of this kind of energy it has (per atom, on average). [9] A hydrogen atom has energy E 5 20.850 eV. Find the maxi- mum possible values for (a) its orbital angular momentum and 14. [10] These first stars lived out their lives creating heavier atoms until the stars had exhausted energy available from fusion and then exploded in events called supernovae which scattered and later became the stuff form which planets were formed. [9] In essence, an atom has a minimum amount of energy it can have (called the ground state); it is against the laws of physics for the atom to have any less energy than this. [9] Just so you are sure, an atom has a certain amount of energy and you do not need to keep adding energy to keep it going any more than you need to add energy to the earth to keep it going around the sun. [9] Lower energy gamma rays from nuclei sometimes overlap what would be called x-rays if they came instead from atoms. [9] Far-ultraviolet rays and X rays from the Sun have enough energy to ionize atoms in the Earth?s atmosphere. [29] The minimum amount of energy that can be gained or lost by an atom is a _. [12] Area 4pr2 With the r terms gone, our expression for the ground-state energy becomes E1 5 2″2/2ma02 5 213.6 eV, where the minus sign shows that the atom is a bound sys- r tem. [10] Collisions transfer energy to neon atoms, exciting them to 54. [10] Since it would therefore take 4.2 eV to separate the atoms, this quantity is called the dissociation energy. [10] If one thing is hot and another cold, the hot one has a higher average energy per atom. [9]

Power is the rate at which the wind delivers energy to your sail and one way to calculate power is the product of the force times the velocity. [9] “There is a vitality, a life force, an energy, a quickening that is translated through you into action, and because there is only one of you in all of time, this expression is unique. [32] The intensity of a wave of light, the rate at which it transmits energy, is proportional to the square of the maximum electric field, that is a wave with twice the amplitude will have four times the brightness. [9] Find the carried in a 30-gauge (0.255-mm-diameter) aluminum super- corresponding (a) frequency and (b) photon energy in eV. conducting wire without the field from that current exceeding 41. [10] For a photon the momentum is proportional to the energy so uncertainty in momentum implies uncertainty in the energy of the photon, not its speed. [9] The same slower speed of the ball initially at rest must be used in the calculation of both the total final energy and the total final momentum. [9] Because both energy and momentum are the function of the same factors (the same masses and the same speeds), neither energy nor momentum can be conserved in the motions of the two balls, contradicting the law of conservation of momentum. [9] Remember, you can always identify work being done by energy changing, and the book moving at constant speed horizontally has constant energy. [9] Exerting a force does not require energy, only if the force does work. [9] The earth does work on it increasing its energy and the air does negative work on it decreasing energy. [9] The instantaneous energy transported by the wave is proportional to the square of the electric field, so no negative energies are introduced. [9] Because covalent bonding within applications. the water molecule leaves the oxygen only slightly negative and the hydrogen only slightly positive, hydrogen bonds are much weaker than ionic or covalent bonds; a typical hydro- gen-bond energy is 0.1 eV. Hydrogen bonds are important in determining the overall con- figuration of complicated molecules. [10] Does it make sense to distinguish individual NaCl molecules in a cohesive energy is 210.5 eV and the value of n in Equation 37.4 salt crystal? What about individual H2O molecules in an ice crys- is 6.25. [10] I understand the equations that explain why energy and momentum is stored in the collision systems. [9] You need to know the de Broglie equation, h / p, and the relation between energy and momentum, E 2 p 2 c 2 + m 2 c 4. [9]

Melting I assume is the breakdown of the crystal lattice and boiling is enough molecules/atoms obtaining enough energy to achieve the vapour state. [9] Go molten salt nuclear, solid state batteries, lots of solar and wind and lots of desalination, for turning deserts green, the only real solution to excess CO2 after all clean energy. [31] Although an equilibrium state may exist, it may not correspond to the lowest possible energy. [29] Its quantized energy states are therefore all bound states. [10] States that can lose energy Energy (eV) -2 4s only by forbidden transitions are metastable states; their lifetimes are many orders of magnitude longer than the nanosecond timescale for allowed transitions. [10]

The space is filled with radiation from all the rest of the universe and the object will eventually be absorbing as much energy as it radiates. [9] No theory yet has managed to explain the behavior of very small objects that also have very high energy, and “this final case is very important if you want to understand where the universe comes from,” says Deffner. [30] Date: March 6, 2018 Source: University of Maryland Baltimore County Summary: Scientists have developed the first techniques for describing the thermodynamics of very small systems with very high energy — like the universe at the start of the Big Bang — which could lead to a better understanding of the birth of the universe and other cosmological phenomena. [30] Sebastian Deffner at UMBC and Anthony Bartolotta at Caltech have developed the first techniques for describing the thermodynamics of very small systems with very high energy — like the universe at the start of the Big Bang — which could lead to a better understanding of the birth of the universe and other cosmological phenomena. [30]

To accomplish this he plans on harvesting the air resistance standard travel applies on the vehicle through something like a wind generator or turbine and solar cells over the cargo area as well as the standard breaking energy reclamation. [9] In more advanced studies we find things like the field actually has energy content, for example an electromagnetic field has an energy density. [9] In fusion (or fission) a small percentage of the mass is converted to energy. [9] If you make mass M disappear, you will make energy appear in some other form to the tune of Mc 2. [9] Now, energy had dimensions of ML 2 /T 2, and mass, of course, has dimensions of M. The only way you can put M and L/T together to get ML 2 /T 2, is M(L/T) 2 and hence mc 2 and not mc or mc 3 or any other combination. [9] Now, the person starts out with an energy of MgH where M is his mass and H is the height from which he jumps. [9] The catch here is that chemistry is an extraordinarily inefficient source of energy and you could never hope to measure the change in mass because it would be so small. [9] The reason is that the warping of space-time (which causes gravity) increases with increasing energy density and a rapidly moving mass has a larger energy density than a slower one. [9] Where does this energy come from? The simple fact is that if you were to weigh the carbon dioxide and compare that weight with the carbon and oxygen you started with you would find less mass. [9] The mass of the helium is slightly less than the sum of the hydrogen masses, and this mass is where the energy comes from. [9] One example is simply the radioactive decay of a nucleus: lost mass is where the energy of the radiation comes from. [9] Incidentally, there actually is a slight increase in the mass because it has increased energy ( m E / c 2 ), but way too small to be able to measure with a scale. [9] Unfortunately, this is an impossible experiment to do because chemistry is such an inefficient way of producing energy that the mass change would be incredibly tiny. [9] Suppose that you get 1,000,000 joules of energy by burning a few pounds of coal; this corresponds to a mass change of 10 6 /(3×10 8 ) 2 which is about 10 -12 kg. [9] Note that this is a very small effect, however, because the mass is so large to start with and a lot of energy takes only a small amount of mass. [9] I estimate roughly that if all the energy from the sun striking the earth were absorbed the mass of the earth would increase by about 1 kg per second. [9] I would expect the mass gain from meteorite collisions to be bigger than from the sun’s energy. [9] Since we understand mass as just a form of energy, it may change into a different kind of energy thereby changing the mass of a system. [9] Since the energy stored is very small, this increase of mass would be impossible to observe. [9] Because helium has a very high binding energy, when fusion occurs the amount of energy released is on the order of 1% of the mass energy of the hydrogen fuel used in the reaction. [9] Einstein?s energy-mass equivalence implies that pair creation of a particle-antiparticle pair is possible, given energy 2mc2 equivalent to the mass of the pair. [10] Emc2 says energy and mass are different manifestations of the same thing. [9] They annihilate completely and their mass is instantly converted into energy. 2. [9] For example if a k shell electron is ejected from the target material (let’s say tungsten) and then if an L shell backfills the void, the ensuing x-ray is 57.4 keV(just the difference in electron binding energies), if M shell fills the void, then 66.7 keV, etc. Then they always give an “effective” energy value, which for k shell is 69 keV. They never explain where this “effective” value comes from. [9] Why electrons, if not static, did not radiate all their energy away was one of the main puzzles of late 19th century physics. [9] There are other energy measures such as the erg (dyne cm(gm cm/s 2 ) cm) and eV (1 electron volt1.6×10 -19 J). [9] The amount of energy released in a single fusion reaction is on the order of a million electron volts and 1 MeV1.6 x 10 -13 joules. [9] The power source gives back the lost energy to the electrons. [9] The highest this energy can be is the energy of the electron beam. [9] As the current is increased through a glow discharge, a stage is reached when the energy generated at the cathode is sufficient to provide all the conduction electrons directly from the cathode surface, rather than from gas between the electrodes. [29] As electrons and holes pour across a forward-biased junction, many recombine; that is, they drop from the conduction band into the valence band, releasing energy in the process. [10] In classical physics, an electron of a given energy can have any angular mo- mentum, up to the maximum of a circular orbit (Fig. 36.6). [10] In the production of characteristic x-rays several texts give the same table of energies indicating the energy of the characteristic x-ray produced for each of the various electron transitions. [9] An electron can have any energy between the top and bottom of a band, but energies in the band gaps are forbidden. [10] An electron in the filled band can?t gain energy unless it?s enough to jump the band gap. [10] Thermal energy readily promotes electrons from these lev- els into the conduction band, greatly increasing the conductivity. [10] We conclude that an electron losing energy radiates electromagnetic energy. [9] This continuum is called bremsstrahlung (German for braking radiation) and results from the fact that electrons are slowing down and hence radiating energy. [9]

Since the rest energy of a proton or a neutron is about 1 GeV1000 MeV, this method would be fairly accurate for up to tens of MeV kinetic energies. [9] QUESTION: I have a question about light and its use for the purposes of creating environmentally friendly energy. [9] QUESTION: Discounting air resistance, does it take more energy to run outside than on a treadmill? Does the motion of the belt pull you along? Are the mechanics of running somehow different on the treadmill? This subject is discussed a lot among people looking to get outside to run this time of year. [9] QUESTION: Is there any possibility of a kinetically powered automobile which stores energy via a dynamo-type generator and transfers it to the engine? Since there are four rotating wheels to most consumer vehicles, the energy could be collected from at least four points. [9] Where did it come from? That question is equivalent to the question “where did the universe come from” because the entire universe contains a certain amount of energy which never changes. [9] QUESTION: I have read that francium has a higher first ionization energy than cesium. [9] ANSWER: First of all, the big rip is highly speculative and relies on dark energy which nobody has any idea what it is. [9] ANSWER: First of all, heat is energy transfer, not energy content. [9]

ANSWER: You are taking your second statement to literally; the use of the word “or” does not imply exclusivity, that is, either or both may contribute to total mechanical energy. [9] ANSWER: I do not know what you mean by gravity “radiates a significant amount of energy”. [9] ANSWER: If you could keep the energy absorbed by the disk from leaving, there would be no difference in the final temperature. [9] The temperature of something is a quantitative measurement of how much internal energy the object has. [9] All objects radiate energy to their environment and the rate of radiation is proportional to T 4 where T is the absolute temperature. [9] Let me outline, from the perspective of energy, what goes on with two objects separated by a large distance. [9] When a player hits a pitch for a homerun does the speed of the pitch at all affect the distance? Will a fastball go further than a slower pitched ball? One camp contended yes, as although some energy was lost at contact with the bat there was still a transfer of energy from fastball to bat. [9] As you note, the source of energy to accelerate to here this speed, not to mention the amount of energy to get significantly closer to light speed, is a real problem. [9] Light itself carries energy at the speed of light; anything else carries its energy at a slower speed. [9] What does efficient mean regarding a light source? We normally think of an incandescent bulb as inefficient because a large fraction of the consumed energy goes into heat instead of light. [9] The energy carried by the absorbed light will show up as a slight increase of temperature of the box. [9] How would you expect the conductivity of an undoped semicon- tational ground state, what energy photon will it emit? ductor to depend on temperature? Why? 13. [10] If C is slower in those materials where do the photons get the energy to return to C(vacuum) once they exit the medium? Is it actually that C does not change and that the photons are refracted and simply take more time to travel through the medium? I sometimes teach radio antenna theory and this is what I’ve always told my students, not that C becomes less. [9] Take that number and divide it by the time for one revolution to get the rate (watts or kilowatts) that energy is being consumed. [9] For each set of quantum numbers there?s an associated energy. [10] In the cubical box, the equal-length sides result in different combinations of quantum numbers with the same energy. [10] Planck’s constant sets the scale for when quantum effects become important for energy. [9] This is in violation of newton, to apply a constant force you need a constant supply of energy. [9] Although such force and energy considerations Equilibrium ultimately govern all molecules, we distinguish several molecular binding mechanisms based on which interactions are most important. 6 separation 4 Ionic Bonding 2 As we saw in Chapter 36, elements near the left side of the periodic table have few elec- 0 r0 trons in their outermost shells and correspondingly low ionization energies. [10] If you double the temperature, you double the average energy of a molecule. [9] If there is degeneracy, there may be several orbitals which comprise the same energy level. [9] Higher energy levels, however, are degenerate, meaning there?s more than one l value for each n. 1. [10] This energy difference is associated with the orien- n 2 level. [10] This effect manifests itself as a separation of what were originally identical energy levels (Fig. 37.12a). [10] There the solid is characterized by an energy-level diagram in which the energy levels are those of Fig. 37.12c at the value r 5 r0 (Fig. 37.13). [10] There, we found that quan- Atomic separation tized vibrational energy levels are given by FIGURE 37.7 Near its minimum, the molecular potential-energy curve approximates a parabola. [10] Vibrational Energy Levels Curve approximatesPotential energy a parabola. [10] The energy between adjacent vibrational levels in diatomic nitrogen is 0.293 eV. What?s the classical vibration frequency 37. [10]

Since E 5 hf 5 hc/l, that volts gives 1.59 eV for CD, 1.91 eV for DVD, and 3.07 eV for Blu-ray. means higher photon energy and therefore a larger band gap. [10] Now, if you view this photon from a different reference frame (moving with respect to the first), the photon will have a different energy as determined by the special theory of relativity. [9] Find the energy of a photon emitted in a transition from the first 53. [10] Just this month it was announced that Atkins will partner with Tokamak Energy to create what they hope will be the world’s first fusion facility (although it will be completed more or less at the same time as France’s internationally-funded model) that generates more energy than it consumes. [31] In empty space a particle-antiparticle pair may come into existence; because of the uncertainty principle, this “energy from nothing” is ok as long as it lasts a sufficiently short time. [9] Every time you compress the tire it costs energy; every time it uncompresses, you get energy back. [9] There are many pairs of conjugate variables in physics, the other best known pair is energy and time. [9] Incidentally, horsepower is not a unit of energy but a unit of power, energy per unit time; the most common unit of power used by physicists is the watt which is a joule/second. [9] For comparison, the entire output of the U.S. is about 10 6 megawatts, about 10 12 watts, so the solar energy is about 200,000 times our current energy output. [9] B?s ground-state energy is 106 times higher than A?s. 35.2. (c), which is almost twice the classical prediction. 35.3. [10] B?s Ka energy should be about four times that of A. X-ray energy (keV) 72. [10] Elements A and B have atomic numbers ZA and ZB 5 2ZA. How do you expect element B?s Ka X-ray energy to compare with that X-ray intensity Pb of element A? As Lb a. [10] Find (a) its energy and (b) the magnitude of its orbital angular momentum. [10] Calculate the value of n1 (by trial and error if necessary) that would produce a series of lines in which: (a) The highest energy line has a wavelength of 3282 nanometers. (b) The lowest energy line has a wavelength of 7460 nm. [9] Calculate dU/dr and d2U/dr2 to show that U has a conduction zone and are thus unavailable for the PV energy conver- minimum, and find expressions for (a) Umin and (b) the separation sion. [10] If all three sides of a qdot are halved, its ground-state energy a. is halved. b. drops to one-fourth its original value. c. doubles. d. quadruples. [10] B?s Ka energy should be about twice that of A. 3 5 7 9 11 13 (b) d. [10]

If there is nothing else around, this system will always have zero energy; this is conservation of energy. [9] The function is sin1nxpx/L2 sin1nypy/L2, with it could equally well be nx 5 ny 5 1, nz 5 2, or nx 5 nz 5 1, ny 5 2, since all three of nx 5 2 and ny 5 1. these combinations give the same energy. [10] In general, how should the energy of an element?s La X rays radiologists reverse the process, exploiting the fact that X rays cause compare with the energy of its Ka X rays? inner-shell transitions as well as complete ejection of inner-shell a. [10]

The general idea is to first drop the ball from a height h above the bottom of the track of radius R and find the speed of the ball at the bottom; we do this from energy conservation. [9] If the energy difference between the ground state and the first ex- 2. [10] If you have no friction and the two strings each are radiating the same sound intensity, the lighter one will die out first since it had less energy to start with. [9] What would be the energy of a gamma ray emitted if a situation? proton in such a nucleus made a transition from its first excited 11. [10]

All objects emit electromagnetic radiation and your teacup is radiating infrared radiation which is invisible to our eyes but nonetheless carries energy. [9] If you choose the falling object as the system, it is not isolated and so energy is not conserved. [9] If you include the air in your system, then as the air takes energy away from the falling object the air must gain that amount of energy which would show up as the air heating up some. [9]

If it interacts with something, though, the light may be absorbed and converted into another form of energy; for example, something on which the sun shines may absorb some of the light and heat up. [9] If you efficiently absorb the light with a black pool liner, the liner itself will warm up and transmit energy to the water both by conduction and by radiation of infrared energy (heat). [9] No light source is 100% efficient; for example a light bulb converts most of its energy to heat, not light. [9] Light provides the energy for the chemistry which happens when the plant grows. [9] For reference, visible light is about 0.2 eV. (eV is an electron-volt, a unit of energy). [9] It cannot disappear because energy is conserved and light carries energy. [9] This is the only way i can descibe the ‘invention’ in my dream, but the end of the dream always becomes a nightmare where the trapped light builds infinitely from being trapped resulting in power that in my dream goes out of control etc. in other words in the experiment the energy engulfs me then i wake up. [9] A German physicist named _ proved that light emission and absorption can only be accomplished in discrete quantities of energy. [12]

ANSWER: Yes, the ionization energy is slightly higher for francium, 380 vs. 376 kJ/mol. [9] ANSWER: Does it take energy to magnetize the bar? Yes, of course; let’s call that energy E. [9] ANSWER: Folks with brilliant ideas for sources of energy often do not take into account the energy cost to create it. [9] ANSWER: Heat is a very special term which refers to energy transfer. [9] ANSWER: The problem is that the radio waves spread out as they travel and the energy gets spread over an ever-increasing area. [9] ANSWER: The energy is not really enormous, it is only relatively enormous. [9] ANSWER: Not unless energy is added to it (for example, have a little bit of plastic explosive stuck to it) or it is thrown down instead of being dropped. [9] ANSWER: You shouldn’t really say more energy, you should say more energy per unit amount of fuel. [9] ANSWER: For nuclei lighter than iron, fission results in a loss of energy, not a gain; that is you must add energy to cause fission. [9] ANSWER: I guess I would reply “why not?” On what are you basing your expectation? Lets look at a greatly oversimplified situation from the perspective of energy conservation. [9] ANSWER: Power density, that is the energy per unit area of the beam. [9] ANSWER: This is a fusion reaction and, for a high probability of the reaction happening, the deuteron should come in with relatively small energy. [9] Your answer? energy emitted as a percentage of the energy supplied to excite 55. [10] Your muscles are doing work and the energy to do this work comes from chemical reactions in you body. [9] Assuming that we know what energy is, work is whatever is done to change the energy of an otherwise closed system. (Actually, heat which is different from work can also change the energy of a system.) [9] The amount of work done is equal to the change in energy, and so work and energy have the same units, joules. [9] Power is something else; it is the rate at which work is done or energy changes. [9] If the gas can expand, as in your example, the energy can also go into work being done by the gas. [9] If the gas expands, it does work, that is it gives back some of the energy added. [9] If you go out instaneously you leave (at t 0) the original wave function sitting there so the energy remains the same, no work done at all. [9] This is how an internal combustion engine works for example; energy is added to the fuel (via chemistry) and the gas both heats up and expands (by moving the piston) propelling the car. [9] Are you doing any work? What is needed to do work? Energy, right? Does it take any energy to hold the book there? It certainly does. [9] Energy in an isolated system is always conserved and does not have to appear as mechanical work. [9] Energy is conserved because there is no work being done by the tension ( T and v are perpendicular). [9] Work done on or by the system on the environment changes the energy of the system. [9] It is not possible for you to move the wall in without doing work thereby increasing the energy of the particle/wave. [9] Still, you must do work because the energy of the system increases; you are the source, again, of the added energy. [9]

For the lowest energy transition, n 2 n 1 +1, so, after a little algebra, n 1 2 ( n 1 +1) 2 /(2 n 1 +1) R 81.85; this is a quadratic equation in n 1 2 and could be solved analytically, but it is probably easier to just make a couple of guesses. [9] Suppose c1 and c2 are solutions of the Schringer equation for the same energy E. Show that the linear combination ac1 1 bc2 14. [10] Substitute the wave function c2 of Equation 36.7 into Equation FIGURE 36.19 Energy-level diagram for the helium-neon laser (Problem 68). 36.4 to verify that the equation is satisfied and that the energy is given by Equation 36.6 with n 5 2. [10] Use Equation 37.5 to calculate the average energy of a conduc- 67. [10] We?ll conclude this chapter with a look at humankind?s attempts to har- ? Describe qualitatively models ness that energy. of nuclear structure (38.1). ? Describe the three common types 38.1 Elements, Isotopes, and Nuclear Structure of radiation, and write equations describing each (38.2). [10]

Torque is not energy, it is the rotational analog of force, so it would be confusing to measure it in joules. [9] It is not the force you use but the energy something has by virtue of that force. [9] It is quite possible to convert a gamma ray into a bunch of low energy photons; this is what a scintillator does. [9] A photon has an energy determined by the frequency of the associated wave, Ehf. [9] A second photon is emitted in the process, with the same energy and phase FIGURE 36.18 Interaction of photons with atomic as the stimulating photon, and in the same direction. [10] Therefore, if you own a radio station you have to continue feeding energy into your antenna for it to continue to send out photons. [9] Show that the wavelength l in nm of a photon with energy E in eV is l 5 1240/E. on a given axis ever equal the magnitude of the angular momen- 32. [10] EVALUATE Photon energy quantization E 5 hf 5 hc/l gives the pho- So Blu-ray data are stored at a smaller spatial scale and thus require ton energy and therefore the required band gap. [10] Photons with more than the band-gap energy give up rmin at the minimum energy. their excess energy as heat, also reducing PV efficiency. [10] In light-emitting diodes (LEDs) and diode lasers, this energy appears as photons whose en- ergy is close to that of the band gap. [10]

QUESTION: Can you describe the energy conversion that occurs when a tennis ball is dropped from waist height to the ground? Maybe you can do better than my teacher. [9] QUESTION: What is the energy balance(Released from-Required for) in the process of nuclear-Fission of Hydrogen and nuclear-Fusion of Uranium. (Why Fission of uranium and Fusion of Hydrogen is so much talked about and not ‘vice versa’). [9] QUESTION: Energy balance question: A physicist is standing on a pier along which a freighter is moving at 10 mph. [9] QUESTION: This has to do with the energy content of gasoline and the energy needed to move a car. [9] FOLLOWUP QUESTION: I still am having difficulty with the energy source of a shorter de Broglie wavelength. [9] My question is, where did the energy come from? My moving of the wall did not add energy to the system. [9]

Gravity waves have been indirectly observed by observing the orbital motion of two massive stars; here the energy of this binary system is systematically decreasing exactly at the rate predicted if gravitational radiation were responsible. [9] I quote: “gravitational perturbations from the giant planet imbued the planetesimals with too much orbital energy for them to accrete into a planet. [9] The problem that I am finding is that the estimated distance using Hooke’s Law is always twice the estimated distance using the conservation of energy. [9] The recent experiments showing the accelerating expansion have led some cosmologists to reintroduce the cosmological constant which is the only “dark energy theory” I am aware of; in any case, the constant is empirical and not really predictive of anything. [9] I also understand the h Plancks constant and that energy is continous but rather in discreet packets, hence quanta. [9]

I’ve told him that his idea might cut down the number of stops, but he will still have to stop thanks to energy lost in the form of heat. [9] Proof: The above outcome is confirmed by the fact that the total final energy cannot be conserved in the above collision. [9] The rotational spectrum of diatomic oxygen shows spectral lines molecule described in Example 37.1. spaced 0.356 meV apart in energy. [10] For the HCl molecule of Example 37.2, determine (a) the energy 19. [10] What happens is that when you heat a gas you add energy to it, that is you make all the molecules in the gas move faster. [9]

That doesn’t mean that if you didn’t put energy in the radio wave that it would just sit there; rather, it would not exist. [9] That ? Describe the curve of binding energy means all nuclei with the same Z belong to the same element. and how it explains energy release in nuclear fission and fusion (38.3). ? Explain nuclear fission and its role as an energy source, including several types of nuclear reactors (38.4). ? Describe nuclear fusion, explaining how it powers the Sun and stars and outlining prospects for terrestrial fusion (38.5). [10]

To get to a very high speed would require a very large energy input and the source would be difficult. [9] You may be assured that no information or energy may be transmitted at a greater speed than c. [9] If you redo the second example for 10% energy loss (0.8 J) you will find the speeds after the collision are about 3.9 m/s (for the struck one) and 0.1 m/s for the incoming one. [9]

In a nuclear reaction, as you note, the energy conversion is much more efficient and masses change by measurable amounts, something like 1%. [9] A gamma ray resulting from a fusion reaction has its energy determined by the reaction, not the environment (like density as you suggest). [9] You have to put energy into the accelerating charges and, if you like, you can think as that energy input as your “impetus”. [9] Would it be like a small snap, or a large bang, or would it incinerate you? Just trying to get an idea of the energy released from a single event. [9] Now they just need to refine the process until they can create more energy than is consumed by the process to create the reactions–something that has never yet been achieved, but is growing closer to becoming a reality each year, thanks to international projects like the one currently taking place in France. [31] As they move with the wave, they are accelerated much like a surfer on a water wave and thus extract energy from the wave, damping it in the process. [29] As the temperature is increased (to around 1500-3000 0 ) the radiated energy shifts so that a significant amount of the energy begins to be emitted at the lowest energy part of the visible spectrum, red, and not much at higher energies. [9] Obviously it requires energy, converting water into steam to create pressure to cook the food at higher temperatures than “normal” air pressure allows. [9] And, there is not that much of a “jet” and what there is quickly dissipates; the energy from this dissipation would show up as a slight increase in water temperature locally. [9] One of the great challenges of humankind is to create these high temperatures in a controlled manner and to harness the energy of nuclear fusion. [29] The temperature is eventually limited by energy losses to the outside environment. [29] At higher temperatures, (up to about 6000 0 or 8000 0 ) the energy is spread out over all the parts of the visible spectrum so the source appears white. [9] In order to increase the temperature of something you have to add energy and this is done by causing heat to flow to it. [9] In empty space there is nothing to absorb this energy so it cannot stop or even slow down. [9] In a bound physical system, energy is quantized, and angular momentum of the system is also quantized. [9] Electromagnetic radiation carries both energy and angular momentum. [9] Neither angular momentum nor energy are conserved as the system radiates. [9]

Here coordinates x, y, z. we show that the ground state has the form of an exponential, and in the process derive the ground-state energy. [10] We?re told the vibra- tional energy state (the ground state, n 5 0), and we need to find the L 5 2pfI 5 12pfI” 5 1fIh 5 1.23310233 J # s rotational state with comparable energy. [10] We?ll deal most thoroughly with the sim- equation to hydrogen and hydrogen- plest atom, hydrogen, and we?ll be more qualitative in describing multielectron atoms. like atoms (35.2). 36.1 The Hydrogen Atom ? We?ll build on the concepts of wave function and probability density, and Like a particle in a three-dimensional box, the electron in hydrogen is confined to a three- we?ll treat atomic electrons as quan- dimensional potential well. [10] The big idea here is that atomic electrons are quantum particles trapped in the 3-dimensional potential well associated with the electric force. [10] For the electron, the well results from the proton?s electrostatic tum particles trapped in the potential attraction. [10]

When the particle is not being observed, it exists as a waveform, which in quantum language represents a state of pure potential, known as superposition. [13] As newborns or infants, if not at conception and in utero, we resemble the infinite possibilities of the wave; our personality, not yet defined, is in a state of potential. [13] The quantum reality exists in what is known as a series of probability waves, with an infinite possibility of potential outcomes. [13] This is, obviously, not a possible situation; one eventually gets into conundrums like this when assuming infinite ( i.e. unphysical) potential barriers. [9] Both the infinite square well and the harmonic oscillator have potential wells of infinite depth. [10]

Sketch the probability density for the n 5 2 state of an infinite n?s are integers and A is a constant. (b) In the process of working square well extending from x 5 0 to x 5 L, and determine part (a), verify that the energies E are given by Equation 35.8. where the particle is most likely to be found. 50. [10] A particle is in the nth quantum state of an infinite square well. well, what?s the well width? (a) Show that the probability of finding it in the left-hand quarter 42. [10]

All matter is made up of tiny, indivisible, indestructible particles called atomos, which are infinite in number and always in motion. [12]

QUESTION: If matter has special qualites at the atom and sub partical levels, such as quantum state. [9] In order to fuse hydrogen atoms into helium, tokamaks must maintain the astronomical level of heat of the plasma (the hottest state of matter) they control. [31] The Bose-Einstein condensate represents a truly new state of matter, in which thousands of atoms join quantum mechanically to behave as a single en- tity. [10] Any matter, being sucked into a black hole, will be subject to enormous forces such that a water molecule will dissociate into its hydrogen and oxygen atoms, those atoms will become ionized, the nuclei will be torn asunder, and even the protons, neutrons, and electrons will lose their identities as they get compressed to a singularity. [9] I say this is total nonsense, a positron is a particle in anti-matter that would be the equivalent of an electron in matter, only with a positive charge. [9] Every particle of normal matter has an antimatter counterpart, equal in mass but opposite in charge. [33] All matter is composed of extremely tiny particles called atoms that can combine in whole-number ratios with atoms of other elements to form compounds. [12] Electron speeds in atoms are nonrelativistic so just doing the Compton effect on normal matter does not require worrying about the electron speed. [9] A teaspoon of nuclear matter has a mass roughly equal to the mass of the Rock of Gibraltar! That ab- surdly high density reaffirms our picture of the complete atom as mostly empty space with its mass concentrated in a tiny nucleus. [10] If classical physics were true then, since the car or baseball have the same mass no matter what the velocity, an uncertainty in the momentum would automatically mean an uncertainty in the velocity. [9]

In 1995 physicists at the University of Colorado first succeeded in producing an assemblage of bosonic matter all in the same quantum state (Fig. 36.14). [10] Nearly all the visible matter in the universe exists in the plasma state, occurring predominantly in this form in the Sun and stars and in interplanetary and interstellar space. [29] The reason that light reaches us over vast distances in the universe is that there is very little matter in space for the light to interact with. [9] ANSWER: Most light moves in empty space or through normal matter. [9] ANSWER: As far as anybody knows there is no such thing as a “dark matter particle” because no such thing has ever been observed. [9] ANSWER: Sorry, but there is no escape from the fact that particles may behave as waves (no matter how “far fetched” you find it!). [9]

A more exotic possibility is that this antimatter is given off by decaying particles of dark matter, the theoretical invisible substance astronomers have so far “detected” only via its apparent gravitational effects on normal matter. [33] My assumption is that the atomic structure of matter is the creator of gravity! Thus you would have denser matter like stuff on a neutron star exhibiting huge gravitational forces. [9] The uniqueness of the plasma state is due to the importance of electric and magnetic forces that act on a plasma in addition to such forces as gravity that affect all forms of matter. [29] It is sometimes referred to as the fourth state of matter, distinct from the solid, liquid, and gaseous states. [29]

ANSWER: First of all, the atoms must be close enough to interact with their neighbors because the phenomena you refer to are the result of collective behavior, the realm of condensed matter physics, so gases are out. [9] ANSWER: What matters is the total amount of current which flows. 100 turns carrying 1 ampere would produce the same field as 1 turn carrying 100 amperes. [9] The appearance of a spot is preceded by the appearance of a magnetic field of 5000 gauss, but which disappears after spots disappearance, betraying the whirligig’s inner move of matter from solar mass, whirligig tube that pass through the solar mass by one hemisphere in another. [31] QUESTION: I know that any matter that has mass generates gravity. [9] QUESTION: Is Teleportation of a living being possible without contradicting Quantum Mechanics in theory ? I know Quantum Mechanics won’t differ between living and non-living matter, but, to my knowledge, Teleportation is the act of getting data of an object, destroying it and then reproducing it. [9] QUESTION: My colleagues and I have a debate about the “speed of light” actually being the upper limit of speed beyond which no matter can travel, based on Einstein’s theory EMC^2. [9] QUESTION: The speed of light is the same no matter what frame of reference it is measured in. [9] If the speed of light is always C then it does not matter how fast the space ship is traveling. [9] I have just proven to him that whatever no matter the weight of 2 objects they both fall at the same speed and both land at the same time. [9] QUESTION: Why hasn’t the asteroid belt condensed or at least started to condense itself into a planet? I was always taught that most planets start as spinning rings of dust and matter (much like the Kuiper Belt) and over time, bada bing, you got yourself a new planet. [9] QUESTION: I have heard of Dark Matter for a long time and i’ve been wondering what it does, what it can do, and how it can be applied to science. [9]

QUESTION: It stands to reason that no matter how far we went into the depths of our universe we would never find an end or wall or boundary of any sort since its my understanding that space is infinity large. [9] The tiniest force will start it moving slowly and then it will go on its own to 5 0 The question you really want to ask is how much torque (it is not just force which matters, but also where you apply it) it takes to give each the same angular acceleration. [9]

From Chapter 22 we know that the electric potential of the proton, treated as a well associated with the electric force point charge e, is V1r2 5 ke/r, with r the distance to the proton and the zero of potential (35.1, 35.3, 20.2, 22.2, 23.1). at infinity. [10] The reason I put voltage in quotes is because the actual value depends on where you choose zero voltage to be; the only meaningful quantity is the potential difference between two points. [9]

Find an expression for the normalization constant A for the wave Section 35.3 Particles and Potentials function given by c 5 0 for ? x ?. b and c 5 A(b2 2 x2) for 2b # x # b. 13. [10] An opposite process, alpha decay, occurs as alpha particles tunnel through a potential barrier that traps them inside large nuclei like uranium. [10] I think it went something like this: A physical system will evolve over time in a path that minimizes the integral (with respect to time) of the Hamiltonian for that system (sum of potential and kinetic energy). [9] A potential source of heat might be supplied by a fusion reactor, with a basic element of deuterium-tritium plasma; nuclear fusion collisions between those isotopes of hydrogen would release large amounts of energy to the kinetic energy of the reaction products (the neutrons and the nuclei of hydrogen and helium atoms). [29] I know the total energy potential of 1 kilogram would be about 90 petajoules (assuming I remember my formulas correctly) This is what I don’t get I know there are 4 binding forces, gravity, electromagnetic, strong, and weak. [9]

I read that you do the work for the magnet when you pick it up to sick it to the roof and you’ll need to do the same amount of work to pry it off again so in essence you have done the work for it and you have simply transferred it to a different potential state. [9] Unless focusing “unlocks” potential heat that would otherwise be masked in light in its regular state. [9] Examples of such barriers include electric potential FIGURE 35.11 Probability densities c21x2 for differences associated with atomic nuclei, gaps between solid materials, and insulating lay- some states of the harmonic oscillator. [10] This event presents a new state of potential and, with it, the possibility of a defining moment, in which the client can break into new terrain. [13]

The very act of observation reduces the wave (potential) to a fixed thing–a particle. [13] Before long, we move from the potential of the wave to the “thingness” of the particle. [13] We are no longer the potential of the wave but the finiteness of the particle. [13]

With the electrostatic probe, ion densities, electron and ion temperatures, and electrostatic potential differences can be determined. [29] The degree of ionization in such plasmas is usually low, but electron densities of 10 1 6 to 10 1 8 electrons per cubic metre can be achieved with an electron temperature of 100,000 K. The electrons responsible for current flow are produced by ionization in a region near the cathode, with most of the potential difference between the two electrodes occurring there. [29] BIOQuantum dots, or qdots, are nanoscale crystals of semiconductor material that trap electrons in a potential well closely resembling the three-dimensional square well discussed in Section 35.4. [10] If a potential difference exists across the plates of a capacitor electrons will flow from one plate and on to the other (not the same electrons) until some limit is reached which depends on only three things, the potential difference, the geometry of the capacitor, and the material which is between the plates. [9] About 10212 s later, a second electron passes through and experiences the potential of the deformed lattice. [10]

Potential difference (voltage) is a measure of the work it takes to move an electric charge from one pole to the other; if the poles are farther apart the field between them is weaker but the distance you must move the charge is farther and the work turns out to be the same. [9] QUESTION: I am trying to convince my uncle that his idea for a potential invention will not work as he thinks it will. [9]

She carried this core belief with her throughout her life, limiting her potential for infinite possibilities. [13] Throughout her life, her thoughts almost automatically continued to affirm this affliction, shutting down her potential for infinite possibilities. [13] Doing so meant that she also needed to embrace her discomfort as she moved beyond the limits of her familiar zone. (As much as we may suffer with our limiting beliefs, we often feel dissonance between our old beliefs and new ones and apprehension about stepping into the new potential and infinite possibility of who we may become when we release the old beliefs.) [13] To access the universal potential, we must devote ourselves to apprehending that infinite possibility, which lies in the instant prior to collapsing the wave with our next thought or feeling. [13] If we continue to summon the same habitual thoughts, we won?t realize the infinite possibilities and potential that await us. [13]

I also know that in Einstein’s EMC squared that as any massive particle approaches the speed of light its mass will become infinite at the speed of light. [9] A large number of electrons are confined to infinite square wells the probability of finding the particle in the left-hand third of the 1.2 nm wide. [10] An electron is trapped in an infinite square well 25 nm wide. of the initial and final states. [10] If this emission is due to electron spectrum emitted by this ensemble of square-well systems? transitions from the n 5 2 to n 5 1 states of an infinite square 52. [10] We needn?t stay stuck in the fixed state of the particle but can ride the infinite possibilities of the wave. [13] Each vibrational level corresponds to an infinite number of rotational states. [10] There is no evidence that electrons or quarks, for example, can be bisected; you cannot bisect something an infinite number of times. [9] To actually draw a field would mean that for every point in space you would have to draw a vector representing the field at that point in space; this is certainly not possible since we can’t draw an infinite number of vectors and they would all overlap each other and make the whole thing just black. [9]

The force between two objects is only exactly zero if they are separated by an infinite distance. [9] Find the probability that a particle in an infinite square well is lo- 35.7 with n 0. (c) Find the normalization constant A0. [10] A particle is in the ground state of an infinite square well. [10] What?s the probability of finding a particle in the central 80% of of the well is an infinite square well, assuming it?s in the ground state? 43. [10]

The infinite square well gives insights into important quantum phenomena shared by more realistic systems such as atoms. [10] An electron is in a narrow molecule 4.4 nm long, a situation infinite square well, find the energies (in eV) of an electron in that approximates a one-dimensional infinite square well. [10] Provided they aren?t too shallow, wells of finite depth also exhibit quantized bound states whose wave func- tions resemble those of the infinite square well (Fig. 35.14), although they show a small but nonzero probability of tunneling into the classically forbidden region outside the well. [10] For Thought and Discussion (mass 60 kg) in a room-sized one-dimensional infinite square well (width 2.6 m), how big would h have to be if your minimum pos- 1. [10]

If you were to go all the way to the speed of light (not possible) an infinite force would be required. [9] This got me thinking; if the wall was straight and infinite and the light was a laser powerful enough to illuminate for a million miles, what happens to the spot of light as the angle of the beam approaches parallel and the illuminated spot is moving along the wall at near light speed or faster than light speed. [9]

The wavelength of these waves at the critical frequency (? p ) is infinite, the electron behaviour at this frequency taking the form of the plasma oscillations of Langmuir and Tonks. [29]

Give a symbolic description for the state of the electron in a hydrogen atom with total energy 21.51 eV and orbital angular momentum 16″. [10] The reason a bound particle cannot have exactly zero kinetic energy is that it would have to have exactly zero linear momentum, so momentum would be exactly known. [9] ANSWER: Well, fusion fuels the sun so look at the sun: an enormous amount of electromagnetic radiation comes out, lots of neutrinos come out carrying kinetic energy, the sun is very hot, that is the particles that make it up have very large amounts of kinetic energy. [9] Another example: kinetic energy is the energy a particle has in addition to its rest mass energy. [9] Since the kinetic energy is much less than the rest mass of either particle, the problem may be treated nonrelativistically. [9] QUESTION: What would be the total kinetic energy of a long, thin rod of length L and mass m which rotates with an angular velocity w and simultaneously has a constant translational velocity v. The rod rotates around an axis which is at the end of the rod, not through the center of mass of the rod. [9] The velocity gets into the equation because of the kinetic energy (moving mass has kinetic energy). [9] The particle is now confined to rebound in one of those two now smaller spaces, thus its de Broglie wavelength is now half of the original, its velocity therefore greater along with its kinetic energy. [9] In an elastic collision, the total kinetic energy of all the particles participating in the collision is the same before and after the event. [29] One of the most important findings is that the temperature of a gas is determined by the average kinetic energy of the particles in the gas, so the slower the particles, on average, are moving the colder the gas. [9] The temperature of a gas is a measure of the average kinetic energy per molecule, so if the atoms were not moving we would be at absolute zero temperature. [9] Thermal energy is, essentially, kinetic energy of the atoms in the object. [9] QUESTION: Could you answer a question to solve an argument I’m having regarding Kinetic Energy? On a web forum, a participant is claiming that an object has an absolute amount of Kinetic Energy, and that this is dependent on all the accelerations it has ever undergone. [9] ANSWER: First of all, they represent different things so why would you expect them to be the same? One is kinetic energy and the other is rest mass energy. [9] ANSWER: First, state the law: The total energy in an isolated system will not change. [9]

Field due to Superconductivity In a metallic conductor, the energy of the highest occupied state at absolute zero supercurrents regions decreasing. is the Fermi energy. [10] What fraction of conduction electrons in a metal at absolute zero have energies less than half the Fermi energy? 48. [10] You?re trying to explain to your classmates how classical and quantum descriptions of electrical conduction in metals differ. ke2 Using copper?s Fermi energy (7.0 eV), you calculate the associ- U 5 2a r0 ated electron speed, then compare your result with the classical thermal speed for an electron at room temperature (300 K). [10] For T. 0, thermal energy promotes some electrons to levels above the Fermi energy, leaving some levels just below EF vacant (Fig. 37.16b). [10] How does the percentage of the number of incident solar photons tion electron at T 5 0 in terms of the Fermi energy. that a PV cell absorbs compare with the energy percentage in the preceding problem? 65. [10]

The atom will, in fact, recoil so that the energy of the photon will be a tiny bit smaller than the energy loss of the atom because the recoiling atom will have a tiny bit of kinetic energy afterwards. [9] If you double the amount of work you double the change in kinetic energy, so you double the change in v 2 if mass is unchanged. [9] If you let it drop from the unstretched spring position, the mass will have its maximum kinetic energy as it passes throught xd and it will continue going down until it gets to x 2 d where it will be momentarily at rest, then go back up, etc. [9] It is a form of energy but, unlike many energy forms, it has no mass and so the only energy it has is its kinetic energy, the energy it has by virtue of its motion. [9] Afterwards there is less mass but more kinetic energy of the fission products. [9] When such reactions lead to the formation of heavier elements, the process is called thermonuclear fusion; mass is transmuted, and kinetic energy is gained instead of lost. [29]

The coldest possible gas (containing no kinetic energy) would be if all the particles were at rest. [9] In an inelastic collision, a fraction of the kinetic energy is transferred to the internal energy of the colliding particles. [29] This implies that the kinetic energy of the particle must also increase. [9]

The expression you give for kinetic energy is only an approximately correct equation at velocities very small with respect to the speed of light. [9] This can occur, however, only by the expenditure of kinetic energy and only if the kinetic energy exceeds the difference between the two energy states. [29] QUESTION: the law of conservation of energy states that the total energy in an isolated system will not change. [9] The big rip, as I understand it, results in an infinite universe in finite time and so a finite amount of total energy spread over an infinite universe would be unobservable. [9] When viewed this way, you take an infinite number of steps but in a finite amount of time. [9] With the Two halfn-xw5ave2lengths infinite square well, for example, an integer number of half-wavelengths can fit in the well, and n is that number. [10] A selection rule for the infinite square well allows only those transitions in which n changes by an odd number. [10] A quantum wire is a conducting structure so thin that quantum els in an infinite square well becomes arbitrarily small compared effects are evident. [10] Treating this system as an infinite square well, determine the ap- cal mechanics must agree in a certain limit. [10]

When you first attach the battery, current will start to flow and so there will be an induced emf (but smaller than the emf of the battery) and as the current gets bigger it will change more slowly until, eventually, a constant current will flow. (The preceding assumes that the inductor itself has some resistance or else a battery would cause infinite current to flow.) [9] The ground state of a system may be measured exactly since it lives for an infinite amount of time. [9] ANSWER: An infinite cylinder is a cylinder which is infinitely long but with a finite radius. [9] The stick would have to be infinitely stiff (impossible) and you would have to exert an infinite force on the other end of the stick (also impossible). [9] The math to calculate it all was “incredibly hard,” Deffner reflects, but the end result, which involved finding a way to compute an infinite number of possibilities, “was actually quite beautiful,” says Bartolotta. [30]

A thicker wire can carry more current than a thinner wire, so a coil with a given number of turns of thick wire has the potential for a higher field than for the same number of turns of thin wire. [9] The effect is to make the P-type material less negative, the N-type less positive, and thus weaken the electric field and lower the potential “hill” that separates the two regions (Fig. 37.19c). [10] AC is not just AC; you need to have an constantly changing potential difference across two wires but what is the potential difference of either of these wires with respect to some other potential we might define as zero? The zero reference potential is usually simply the earth, that is we drive a steel stake into the ground and define that potential to be zero. [9] Note that the neutral wire, even though it is always at zero potential, will carry electric current and is therefore sometimes called the return. [9] If you short with a true zero resistance (superconductor), either the potential difference must drop to zero or the wire must go nonsuperconducting. [9]

ANSWER: No. The poles of a AA battery have a potential difference of about 1.5 volts regardless of their separation. [9] ANSWER: I won’t judge how practical or efficient it is, but two dissimilar metals which form a junction will generate a potential difference across the two when heated. [9] ANSWER: Quite simply, your instrument was not sensitive enough to measure the voltage, but if a current was flowing and the wire was not a superconductor, there was a potential difference but it was likely small. [9]

The “voltage” at the point depends on the potential difference which you have set between the point and the plate, for example by attaching a battery or power supply between them. [9]

Why is it that the earth, or any other planet for that matter doesn’t eventually spin tighter and tighter circles and eventually get absorbed or crash into the Star (sun)? Partial answer resolved: since I am not an idiot and I have given this some thought, I did reason to the point that the answer must have something to do with the fact that we are spinning in the opposite direction on our axis compared to what one might expect. [9] ANSWER: I am not sure I have the picture of what you are doing but it is likely that what matters is the speed of sound in the liquid, not the density of the liquid. [9] The answer was that black holes would not consume the entire universe because they only swallowed matter which moved across their event horizons. [9] The matter density distribution is a description of how the mass of the nucleus is distributed. [9] What if general relativity is not exactly correct for very large distances (much larger than our solar system)? In other words, what if we do not understand gravity as well as we think we do? In that case, the funny way gravity appears to behave might be perfectly normal and not require “inventing” a new kind of matter at all. [9] If matter has different qualities at the macro level, the stuff we interact with. [9] Then does matter take on different properties at the jumbo level/galatic level, such as star systems and galixes. [9]

Astrophysicists say that there must be some new kind of matter which interacts only via the gravitational force with other matter. [9] It is really the impulse that matters, that is you could exert a small force over a very long time and alter the orbit. [9] Now suppose the pipe had a section where it got three times larger; in this larger region the water would slow down considerably, but there would still be 5 gallons per minute flowing through the pipe no matter where you looked at it. [9] Some- times the same underlying matter may assume different structures, depending on how the solid was formed; this is the case with diamond and graphite, both crystalline forms of carbon. [10]

The ETHER is a physical reality constituted from a very small matter, invisible for human eye, and is formed from atoms more small with 7. 8 order of dimension than the atoms of the chemical elements. [31] QUESTION: In the famous youngs double slit experiment it was concluded that matter alters via conscious observation. this happens via probability fields being flattened. [9] The relative magnitudes of the electric and magnetic fields are fixed; they have been drawn to have equal magnitudes here to make the picture easy to look at but they are, in fact, not even measured in the same units so it does not really matter what the relative magnitudes are in a picture like this. [9]

You will note that no matter what the temperature and pressure are, if you keep the temperature of liquid water constant and increase the pressure, the liquid will never solidify. [9] What matters is the rate of change of temperature as a function of temperature difference. [9]

ANSWER: Your “conservation of matter” is an antiquated idea. [9] There is a nice answer on WikiAnswers which essentially says that it is probably not measureable and does not matter anyway. [9]

QUESTION: What is the largest proof of dark matter so far? (My friend and I are doing a science fair project on the topic). [9] QUESTION: A coworker and I have a disagreement over the law for the “Conservation of Matter”. [9]

Further in the past galaxies were moving away from each other faster? I thought I heard recently that the universe was thought to be speeding up due to the influence of dark matter. [9] It has become very widely accepted that there must be some kind of exotic matter in the universe which interacts only through gravity. [9] Jan. 13, 2016 – After the Big Bang, the Universe expanded and, by cooling down, the matter progressively took shape. [30] Now they are closing in on this strange bombardment’s source, tentatively linking it with the enigmatic dark matter thought to make up roughly five sixths of all matter in the universe. [33] There are many aspects of the the observable universe which suggest that there is far more matter than we observe. [9] Isn’t the same true for other waves such as sound? No matter how fast a train is moving, its sound waves still travel at sound speed. [9] The matter of the ether penetrate in all the visible bodies and is the physical matter which fills both the interplanetary space and the interatomic space. [31] Such a huge collection of matter is bound to have some net angular momentum so that the whole cloud has a very small net spin around the center as it collapses. [9]

It is shown in any elementary physics text that this work increases the kinetic energy of the object by an amount equal to the work done by the weight. [9] I and others claim Kinetic Energy is a relative value, as is Velocity, and that the same object will have different Kinetic Energy depending on the Frame Of Reference of the observer. [9] It is only if you cannot locate a stationary point about which the object is actually rotating that you need to include translational kinetic energy. [9] Kinetic energy is something an object has by virtue of its motion. [9]

As you note, the energy carried off will have to come from the electron which then will slow down and eventually run out of energy to radiate away (but this is just its kinetic energy which goes away). [9] Space is not a perfect vacuum and so it can have a temperature which is usually defined as being a measure of the average kinetic energy per molecule. [9] If the balloon were rigid, the energy would all go into the kinetic energy of the gas; the result would be that the pressure of the gas would be larger because the molecules would exert more force on the walls when they collide with it. [9] The work must increase the energy of the gas and the only way to do that (for a monotonic ideal gas) is to increase the kinetic energy of the molecules. [9] Burning twice the fuel will give twice the work (energy) so the kinetic energy increases by a factor of two and the velocity increases by a factor of 2. [9] Now the conservation principle says that the change in the kinetic energy is proportional to the work done one it. [9] The work is equal to the increase in kinetic energy: WFs½ mv 2. [9]

All collisions will be completely elastic unless the kinetic energy of some atoms is larger than the minimum energy required to excite such an atom (likely only for extremely hot gases). [9] When the spring atoms come apart, they start a little closer to each other than they would if the spring were not compressed, so they move a little faster when they leave and so the average kinetic energy of all the atoms is a little larger than it would have been for the uncompressed spring. [9]

Kinetic energy is not a conserrved quantity here, that is the bullet starts with zero kinetic energy to the observer on the ground but a high kinetic energy to the observer on the jet. [9] Most of this heating comes from the fan itself heating up (primarily the heating of the electric motor) not from the small kinetic energy given the air molecules in the “wind” since these drift velocities are generally small compared to the average speed of molecules in the air. [9] ANSWER: Energy takes many forms, one of which is kinetic energy, the energy something has by virtue of its motion. [9] ANSWER: You do not want to say “how much kinetic energy does it produce” because it has kinetic energy which it then loses when it hits the target. [9] ANSWER: You have only a small error here — the kinetic energy of the car is about 400,000 J, not kJ, so the required gasoline is only about 0.003 gallons. [9] ANSWER: The large ball, which has much more kinetic energy than the small ball upon impact with the floor, transfers some of its kinetic energy to the small ball. [9]

If a force of air is compressed into a cylider via a piston that pushes the air through a small air nossel and propels a.2 gram bb at 300ft/s is that the same amount of kinetic energy as 3.4 gram bbs propelled simarly down a barrel at 237ft/s? The 3.4g bbs are lined up touching each other. [9] Since they are not infinitely separated, they exert forces on each other and start accelerating toward each other, so each acquires a kinetic energy. [9]

The question should be how much kinetic energy does it have just before hitting the target. [9] A car driving down the road has kinetic energy which means that, to get it moving you must give it that energy. [9] I’m guessing an electric motor could start the vehicle, and be used intermittently during traffic stops, with the kinetic energy propelling a light-weight auto on stretches road that don’t require frequent stops, like highways. [9] In your example the hot teacup is losing its kinetic energy by increasing the temperature of its cooler environment; this is called cooling by conduction. (Convection, currents of air and tea, also plays an important role.) [9] Kinetic energy of the wave goes into heat mostly; but you don’t really notice it since there is so much sand and water and the temperature increase will be immeasurably small. [9]

Classically, a particle whose total energy is lower than curves are classical predictions. [10] Keep in mind that energy is total energy (that is, including rest mass energy). [9] Because the only force on the pendulum bob does no work, because it is always perpendicular to the motion, the total energy of the system never changes, that is it is conserved. [9] The total energy of the pair is then 4.2 eV below that of neutral chlorine and sodium atoms at large separation (Fig. 37.2). [10]

Use the result of Problem 47 to determine the Fermi energy for cal- dimensional crystal consisting of an evenly spaced line of alter- cium, which has 4.631028 conduction electrons per cubic meter. nating positive and negative ions (Fig. 37.24). [10] The Fermi temperature is defined by equating the thermal energy kT to the Fermi energy, where k is Boltzmann?s constant. [10] The Fermi energy in metals is much higher than the thermal en- ergy at typical temperatures. [10]

ANSWER: Total energy of an isolated system is always conserved. [9] It is more likely to emit many photons as it falls but their total energy would have to be the same as the single 91 nm photon. [9] Now, what is conserved in an isolated system? The two important things are total energy and total linear momentum. [9] The first law of thermodynamics is simply conservation of energy: the total energy of an isolated system must remain unchanged, that is you can never get something for nothing. [9] Your first sentence is a statement of conservation of energy: the total energy of an isolated system never changes. [9]

At some point, we need to stop choosing to believe the meaning we ascribed to our past and script a different present that opens us up to infinite possibilities. [13] In the space between our thoughts, we are similar to the wave–full of infinite possibilities. [13]

Because the atoms of such alkalies as potassium, sodium, and cesium possess low ionization energies, plasmas may be produced from these by the direct application of heat at temperatures of about 3,000 K. In most gases, however, before any significant degree of ionization is achieved, temperatures in the neighbourhood of 10,000 K are required. [29]

Considering the universe to be approximately uniform, one can show that the total negative gravitational energy in it would exactly cancel out the total positive energy represented by matter. [14] To accomplish this, time machines often are thought to need an exotic form of matter with so-called “negative energy density.” [34] In a way, of course, we might argue that the energy of the universe (including matter, as one form of energy) has always existed and always will exist since, as far as we know, it is impossible to create energy out of nothing or destroy it in nothing. [17]

Another theory for potential time travelers involves something called cosmic strings — narrow tubes of energy stretched across the entire length of the ever-expanding universe. [34] “That far along? And I have a potential solution for the energy issue that I am pretty confident will work, but it wont become available for some time yet, potentially years,” I said, thinking about the pyro known as Scorch. [35] Taoism calls this universal energy the Tao, which is described as having no characteristics, yet it is not nothingness because it contains all potential for life. [36]

If a particle having negative energy falls into the black hole, it will cause the black hole’s mass to decrease. [14] Now, as there is only a small space present in between the metal plates, a limited number of particles having negative energy are able to manifest there. [14] Since the entire system was originally in a state of zero energy and no positive energy was introduced into it, the energy expended in doing the work of moving the plates together must be negative. [14]

What differs is the amount of energy needed to accelerate the mass to achieve escape velocity: The energy needed for an object of mass to escape the Earth’s gravitational field is GMm / r, a function of the object’s mass (where r is the radius of the Earth, G is the gravitational constant, and M is the mass of the Earth). [15] Consequently the energy needed to lift an object of mass m from height s above the Earth’s center to height s + ds (where ds is an infinitesimal increment of s ) is gm ( r / s ) ds. [15]

If you look even closer, atoms and other particles in their basic form are only made up of energy. [36] Without the presence of any energy or application of any external force, spontaneously the two parallel plates move closer, until the distance between them becomes zero and they touch each other. [14] The Equinox Singularity exits in zero point energy – the balance point between opposing forces. [16]

These vortices are invisible to the human eye, and like all energy, they have no mass or physical structure. [36] That means if you look closely enough at any person, plant or even an object like a rock, its basic structure is nothing more than a collection of spinning energy vortices. [36] More massive objects require more energy to reach escape velocity. [15]

This was the first time physics had indicated towards the existence of negative energy. [14] The following are a few examples which highlight the importance of negative energy in the modern times. [14] Though his equation predicted the existence of negative energy, Dirac was unable to experimentally verify this prediction. [14] In the following sections, we shall explore what negative energy in quantum physics is. [14] Negative energy is a proven fact in physics that is known to exist all around us and everywhere in the Universe. [14] Negative energy is gravitationally repulsive, and hence using it, a wormhole can be kept open, making room for the possibility of interstellar space travel. [14] Negative energy is a mysterious concept in the world of physics that appears to be more suited to the pages of a science fiction novel than in real life. [14] Negative energy remained only a theory until in 1948, Hendrik Casimir proposed an experiment which could display the effects produced by negative energy. [14] Casimir argued that if the effects of gravity and electromagnetism were ified, a nearly pure vacuum would be created within which, the effects of negative energy would manifest in an observable manner in the form of something known as the Casimir effect. [14] The Casimir effect proves the existence of negative energy density in a vacuum. [14] The concept of negative energy comes as a solution to this problem. [14] The concept of negative energy, however, provides a way around this problem by allowing for the possibility of creating a warp drive. [14] Among the several befuddling concepts that have over the years arisen from the uncertainty principle, negative energy is one of them. [14] He did propose that if an ideal vacuum could be created wherein all effects of positive energy were eliminated, then the presence of the Dirac sea and therefore of negative energy could be verified. [14] According to Dirac, negative energy exists all around us, but its presence cannot be determined since it is balanced out by the positive energy present everywhere. [14] This cast a large shadow of doubt on the very concept of negative energy. [14] Since its conception and experimental verification, the concept of negative energy has gone on to become an integral part of modern physics. [14] In order to explain this, Hawking stated that the production of positive energy in the form of radiation from the black hole, was accompanied by the flow of negative energy into it, thus leading to the conservation of energy. [14] Another important concept where negative energy plays a vital role is the curvature of space-time, known as the wormhole. [14] Calculations have shown that negative energy would be required to create and maintain the warp bubble. [14]

She still had no clue how to stabilize it, or to even limit the energy draw – and we still werent sure where the energy for Extremis was even coming from – to a level that was survivable, but progress was being made. [35] Emanating from zero dimension and zero volume, the pulse of singularity activates a swirling torus continuum of energy. [16] When you look closer still, physicists believe there is a field of energy that permeates the universe called the Higgs field. [36] All effects of external positive energy and force have been removed or ified. [14] My real work is on trying to handle the energy issue; there is just too much of it, and I cant come up with any way to regulate the flow.” [35] I couldnt manage vibranium nanites, not until I could figure out how to interact with the energy stored inside the individual vibranium molecules, but I could manage an excellent super-suit. [35] I mean, I dont even know where to begin when it comes to tracing the energy flows beyond the physical. [35] The phenomenon of escape velocity is a consequence of conservation of energy. [15] The simplest way of deriving the formula for escape velocity is to use conservation of energy. [15]

This is what lies beneath all matter, and interacting with the Higgs field is what gives atoms and other particles their physical mass. [36] Defined a little more formally, “escape velocity” is the initial speed required to go from an initial point in a gravitational potential field to infinity with a residual velocity of zero, with all speeds and velocities measured with respect to the field. [15]

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6. (27) The Concept of Negative Energy in Physics Simplified for You

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9. (21) Properties of the solutions to the Schringer equation – Chemistry LibreTexts

10. (21) Potential energy and internuclear distance | Physics Forums

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17. (11) Mass-Energy – The Physics Hypertextbook

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