I Can an atom absorb a photon, yet its total kinetic energy is decreased?

[avicenna]

Let's assume an atom consists of the nucleus and electrons as point particles. Take the inertial frame to be that of the fixed laboratory. Its total energy consists of the total kinetic and potential energy of the system of particles.If an electron absorbs a photon of energy E, the total energy of the atom increases by E. Can it happen that this increase in energy result in an increase of its total potential energy = E + Del(potential energy) and its total kinetic energy decreases by Del(potential energy).

 

[DrClaude]

First, it is not the electron that absorbs the photon, it is the system nucleus + electron.

Otherwise, I am not sure what you are after. If you take the atom as a whole, then yes its kinetic energy can decrease. As the photon carries momentum, if the atom was moving initially in the direction opposite to the photon, then the kinetic energy of the atom will decrease.

If you are taking about the internal states, then the answer is no. The viral theorem tells you that for the Coulomb potential, you have
$$
2 \braket{T} = - \braket{V}
$$
so the magnitude of kinetic energy and the potential energy must vary in lockstep.

 

[avicenna]

"First, it is not the electron that absorbs the photon, it is the system nucleus + electron."

But the wiki seems to state otherwise:
(Bohr's theory)
"Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels according to the Planck relation:

 

[Andy Resnick]

Let's assume an atom consists of the nucleus and electrons as point particles. Take the inertial frame to be that of the fixed laboratory. Its total energy consists of the total kinetic and potential energy of the system of particles.If an electron absorbs a photon of energy E, the total energy of the atom increases by E. Can it happen that this increase in energy result in an increase of its total potential energy = E + Del(potential energy) and its total kinetic energy decreases by Del(potential energy).

If I understand your question, the answer is 'yes', it's the basic principle of laser cooling- cooling atoms via laser light.

 

[PeroK]

"First, it is not the electron that absorbs the photon, it is the system nucleus + electron."

But the wiki seems to state otherwise:
(Bohr's theory)
"Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels according to the Planck relation:

Spectroscopy applies to atoms, not to electrons. It's very much the atom that is absorbing and emitting radiation in discrete wavelengths.

 

[berkeman]

But the wiki seems to state otherwise:
(Bohr's theory)
"Electrons can only gain and lose energy by jumping from one allowed orbit to another

Orbit around what?

 

[avicenna]

Orbit around what?

But it is what the wiki says and how the textbook explains Bohr's theory, a classical theory. If you insist we should not invoke Bohr's theory, then I have no comment.

 

[berkeman]

But it is what the wiki says and how the textbook explains Bohr's theory, a classical theory. If you insist we should not invoke Bohr's theory, then I have no comment.

Say what? You seem to be misinterpreting the responses you've received in this thread, and misunderstanding the wiki article. The energy of the photon is absorbed by the system of the electron and the nucleus that it is bound to. That *system* is what can absorb that photon energy (given the right circumstances). It is not a free electron that is absorbing the energy.

Have any comments on that?

 

[avicenna]

Say what? You seem to be misinterpreting the responses you've received in this thread, and misunderstanding the wiki article. The energy of the photon is absorbed by the system of the electron and the nucleus that it is bound to. That *system* is what can absorb that photon energy (given the right circumstances). It is not a free electron that is absorbing the energy.

Have any comments on that?

Bohr's theory is clear about how an electron of an atom (nothing about free electrons) absorbs a photon; the electron goes to a higher energy state.

 

[Ibix]

Bohr's theory is clear about how an electron of an atom (nothing about free electrons) absorbs a photon; the electron goes to a higher energy state.

But the energy states aren't something the electron has on its own. In the Bohr model, the energy states correspond to different orbits around the nucleus. So it's the atom that absorbs the photon; the electron doesn't have "higher energy states" without being part of an atom.

 

[avicenna]

But the energy states aren't something the electron has on its own. In the Bohr model, the energy states correspond to different orbits around the nucleus. So it's the atom that absorbs the photon; the electron doesn't have "higher energy states" without being part of an atom.

The electron's total energy (kinetic + potential ) increases by E = h f

 

[Ibix]

The electron's total energy (kinetic + potential ) increases by E = h f

If so, the nucleus doesn't change its state of motion because there's no energy to spare. Right?

Or it's possible that you are considering a model that is a bit too idealised (assuming the nucleus is effectively an infinite mass) to answer the question you are asking.

 

[PeroK]

The electron's total energy (kinetic + potential ) increases by E = h f

What about conservation of momentum? When an atom emits a photon, it's the atom that recoils; not the electron.

 

[berkeman]

The electron's total energy (kinetic + potential ) increases by E = h f

Here, this should clear things up for you a bit...

https://en.wikipedia.org/wiki/Electron_configuration

 

[avicenna]

If so, the nucleus doesn't change its state of motion because there's no energy to spare. Right?

Or it's possible that you are considering a model that is a bit too idealised (assuming the nucleus is effectively an infinite mass) to answer the question you are asking.

The energy absorbed by the electron is E=hf; it is the increase in the total energy of the electron relative to the mass-center (kinetic+potential).

 

[avicenna]

What about conservation of momentum? When an atom emits a photon, it's the atom that recoils; not the electron.

Correct.

 

[Ibix]

The energy absorbed by the electron is E=hf; it is the increase in the total energy of the electron relative to the mass-center (kinetic+potential).

So where do you think the energy to start the atom moving (or change its state of motion) comes from?

 

[Herman Trivilino]

"First, it is not the electron that absorbs the photon, it is the system nucleus + electron."

But the wiki seems to state otherwise:
(Bohr's theory)
"Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels according to the Planck relation:

Bohr's theory is part of the old quantum theory and only works in special cases. Anyway, it's the atom, not the electron, that absorbs or emits radiation.

 

[sophiecentaur]

Bohr's theory is clear about how an electron of an atom (nothing about free electrons) absorbs a photon; the electron goes to a higher energy state.

I wouldn't say that the wording of the version of Bohr's theory that you remember is clear because that statement ignores the need for a photon to interact with the system. We have moved on from there to deal with many other forms of energy changes in quantum systems of charges.
There really is very little point in trying to resurrect early models and insist they must be correct.

 

[Dale]

The electron's total energy (kinetic + potential ) increases by E = h f

The potential energy belongs to the atom, not the electron. The electron doesn’t have potential energy in its own. The potential energy describes the relationship between the electron and the nucleus, which is the atom.

 

[PeterDonis]

the wiki

Is not a good source to be using, you should be looking at textbooks or peer-reviewed papers.

(Bohr's theory)

Is an outdated model. You want to be looking at a modern treatment. There are many good textbooks that cover this material.

 

[PeterDonis]

how the textbook

What textbook? The only specific source you've mentioned is Wikipedia.

explains Bohr's theory, a classical theory.

No, Bohr's theory is not a classical theory. It was an early version (now outdated, as I have said) of quantum theory.

If you insist we should not invoke Bohr's theory, then I have no comment.

Why would you want to use an outdated theory when there are good modern treatments of the same thing?

 

[avicenna]

The potential energy belongs to the atom, not the electron. The electron doesn’t have potential energy in its own. The potential energy describes the relationship between the electron and the nucleus, which is the atom.

You set me thinking. I can't yet give you a proper reply now - probably later.

I have some observations to make relating to the solar system. You would then
say the earth does not have potential energy on its own, only the solar system
has potential energy. But in the real world, we calculate the system of the
earth and the sun only and its "approximation" seems to be good enough.

In Bohr's theory, there was only one electron of the hydrogen atom, so ok. In
many-electron atoms, you expect me to include potentials between electrons. Are
you not asking me to solve a n-body problem, n > 2,3,4...No one has yet solved
the 3-body problem

 

[avicenna]

What textbook? The only specific source you've mentioned is Wikipedia.No, Bohr's theory is not a classical theory. It was an early version (now outdated, as I have said) of quantum theory.Why would you want to use an outdated theory when there are good modern treatments of the same thing?

I only know Bohr's theory. Tell me if my reliance on it misled me into wrong conclusions.

 

[PeterDonis]

I only know Bohr's theory. Tell me if my reliance on it misled me into wrong conclusions.

As far as I can tell, you aren't even using Bohr's theory correctly. More generally, you don't seem to understand how potential energy works.

You would then
say the earth does not have potential energy on its own, only the solar system
has potential energy. But in the real world, we calculate the system of the
earth and the sun only and its "approximation" seems to be good enough.

Sure, the Earth-Sun approximation works for many purposes. But you aren't even doing that. You're trying to make sense of the potential energy of just the Earth alone--that's what asking for the potential energy of the electron is analogous to.

In
many-electron atoms, you expect me to include potentials between electrons

Nobody is asking you to do that. Everyone keeps telling you that the potential energy, even for a one-electron atom, is not a property of the electron. It's a property of the atom. That is, the electron-nucleus system. Analogous to the Earth-Sun system.

 

[PeterDonis]

No one has yet solved
the 3-body problem

Here you're talking classical physics. Atoms are not classical objects. They are quantum objects. For quantum objects we don't even have an exact general solution for the two- or even one-body problem. Indeed, in quantum field theory, where the vacuum state itself is complicated, we don't even have an exact solution for the zero-body problem. But none of that prevents us from constructing models that make accurate predictions, even if one has to use successive approximations to do it. The question is what approximations to use.

 

[Dale]

You would then say the earth does not have potential energy on its own, only the solar system has potential energy.

Yes.

But in the real world, we calculate the system of the earth and the sun only and its "approximation" seems to be good enough

Sure. Although you do have to specify the exact purpose for which a given approximation is considered good enough.

you expect me to include potentials between electrons. Are
you not asking me to solve a n-body problem, n > 2,3,4...No one has yet solved

I am not expecting or asking either. I am simply telling you that the PE belongs to the atom, not the electron.

This is important because an electron has no internal structure so it cannot absorb a photon at all. It can only scatter the photon.

 

[sophiecentaur]

You would then
say the earth does not have potential energy on its own,

Potential energy is always relative to some frame. It takes two to do the PE tango.

 

[avicenna]

Potential energy is always relative to some frame. It takes two to do the PE tango.

It is just debating on semantics. An electron coming to a proton from infinity has PE = -K/r. Its total energy relative to proton (theory same for mass center ) T = PE + 1/2 mv², v is relative velocity to proton. The textbooks do identity "a potential energy of an electron".

 

[sophiecentaur]

It is just debating on semantics. An electron coming to a proton from infinity has PE = -K/r. Its total energy relative to proton (theory same for mass center ) T = PE + 1/2 mv², v is relative velocity to proton. The textbooks do identity "a potential energy of an electron".

Your problem here is a matter of degree. For two equal masses and charges, neither mass 'has PE'. So where's the difference when it's an electron and a proton?
That is not semantics.

 

[vanhees71]

"First, it is not the electron that absorbs the photon, it is the system nucleus + electron."

But the wiki seems to state otherwise:
(Bohr's theory)
"Electrons can only gain and lose energy by jumping from one allowed orbit to another, absorbing or emitting electromagnetic radiation with a frequency determined by the energy difference of the levels according to the Planck relation:

Bohr's theory is outdated for 98 years now. To be honest, it never was a real theory, and it worked thanks to the shear luck of the large dynamical symmetries for the harmonic oscillator as well as the hydrogen atom. For almost everything else it failed dramatically. It even fails on very simple qualitative grounds: The hydrogen atom is not a little disk but a sphere in its ground state as the chemists well know.

 

[Dale]

It is just debating on semantics.

It actually isn’t. It has real experimental consequences. If the electron on its own had PE then a free electron could absorb a photon. But we experimentally see that electrons cannot absorb photons, they can only scatter them.

Atoms can absorb them because PE belongs to the atom, but not electrons because they don’t have PE on their own. Since your question is specifically about the absorption of a photon, not only is this distinction not merely semantics, it is directly relevant to the specific question you asked.

 

[Dale]

Can it happen that this increase in energy result in an increase of its total potential energy = E + Del(potential energy) and its total kinetic energy decreases by Del(potential energy).

For a direct answer to your question see here:

https://physics.stackexchange.com/q...-total-kinetic-energy-decreased/783085#783085

The KE decreases for any $$v<\frac{-E^2-4Em}{E^2+4Em+8m^2}$$

 

[PeterDonis]

It is just debating on semantics.

No, it's not. An isolated electron is physically different from an electron in a bound system. Treating them as though they are the same does not work.

The textbooks do identity "a potential energy of an electron".

Please give a specific reference, with context. I strongly suspect you will find that the context is an electron in a bound system with a proton or atomic nucleus, and that the context makes it clear that the potential energy is a property of the bound system, not the electron in isolation.

Please do not make further assertions along these lines without taking some time to read valid references carefully. This point has already been belabored too long in this thread.

 

[avicenna]

No, it's not. An isolated electron is physically different from an electron in a bound system. Treating them as though they are the same does not work.Please give a specific reference, with context. I strongly suspect you will find that the context is an electron in a bound system with a proton or atomic nucleus, and that the context makes it clear that the potential energy is a property of the bound system, not the electron in isolation.

Please do not make further assertions along these lines without taking some time to read valid references carefully. This point has already been belabored too long in this thread.

I have never ever said that an electron on its own can have potential energy. I only said it is a matter of semantics whether we associate the amount of energy to the electron or to tha atom(the system). The amount is the same!

From my physics textbook, pg 984:
... The further the electron is from the nucleus, the greater is its potential energy; or less negative is its potential energy.

From: University of Tennessee, Knoxville
http://labman.phys.utk.edu › modules › Electric potential

(Lecture 4: Electrostatic Potential, Electric Energy, eV, Conservative Field, Equipotential Surfaces)

http://labman.phys.utk.edu/phys222core/modules/m2/Electric potential.html#:~:text=The potential energy of the,energy and its potential energy.
Problem solving:
Reasoning:
The force on the electron is the Coulomb force between the proton and the electron. It pulls the electron towards the proton. For the electron to move in a circular orbit, the Coulomb force must equal the centripetal force. We need keqe2/r2 = mv2/r.

Details of the calculation:
mv2 = keqe2/r, so the kinetic energy of the electron is
KE(r) = ½mv2 = ½keqe2/r.
The potential energy of the electron in the field of the positive proton point charge is U(r) = -qeV(r) = - keqe2/r.
The total energy is the sum of the electron's kinetic energy and its potential energy.
KE(r) + PE(r) = -½keqe2/r = (-½) (9*109)(1.60*10-19) /(5.29*10-11) J = -2.18*10-18 J.

Do I need to make further clarifications?

 

[sophiecentaur]

I only said it is a matter of semantics whether we associate the amount of energy to the electron or to tha atom(the system). The amount is the same!

The fact that a proton has 2000 times the mass of the electron means that you can treat the proton as 'stationary' in a mechanical collision - but that's all. Your arguing would need to change direction rapidly in the case of a diatomic molecule absorbing a photon which has energy corresponding to a change in vibrational energy. So why not talk in a consistent way, rather than hanging onto a wording that's around 100 years old to back up your preferences?

 

[Vanadium 50]

Please give a specific reference, with context

The old classic, "My Physics Textbook". Page 984.

You seem to be getting upset. The problem isn't that the OP hasn't read the answer, it's that he doesn't believe the answer. That's not something we can fix.

Sure, there will likely be negative consequences down the road, but maybe that will provide the necessary impetus for a change of his perspective.

 

[Dale]

We need keqe2/r2 = mv2/r.

Details of the calculation:
mv2 = keqe2/r, so the kinetic energy of the electron is
KE(r) = ½mv2 = ½keqe2/r.
The potential energy of the electron in the field of the positive proton point charge is U(r) = -qeV(r) = - keqe2/r.

As you mentioned “in the real world” to me earlier, I will do the same here. In the real world people, including textbook authors, often say one thing and do another. Although this author said “energy of the electron” note what they actually did in the math.

First, they used the variable $r$. In context, $r$ describes the atom, it is not the radius of the electron nor the radius of the nucleus, it is the radius of the atom.

Second, $m$ in the KE formula is constant. If the PE belonged to the electron then as it gained PE it would also gain mass. Since an electron is so small, this would be noticeable, small but noticeable.

So although in English they say “potential energy of the electron” in math they actually do “the potential energy of the atom”.

 

[avicenna]

As you mentioned “in the real world” to me earlier, I will do the same here. In the real world people, including textbook authors, often say one thing and do another. Although this author said “energy of the electron” note what they actually did in the math.

First, they used the variable $r$. In context, $r$ describes the atom, it is not the radius of the electron nor the radius of the nucleus, it is the radius of the atom.

Second, $m$ in the KE formula is constant. If the PE belonged to the electron then as it gained PE it would also gain mass. Since an electron is so small, this would be noticeable, small but noticeable.

So although in English they say “potential energy of the electron” in math they actually do “the potential energy of the atom”.

I surrender!

My level of physics has not reached the level where the mass of the electron may change. Give me time to do some catch-up!!!

 

[PeterDonis]

I have never ever said that an electron on its own can have potential energy. I only said it is a matter of semantics whether we associate the amount of energy to the electron or to tha atom(the system).

You're quibbling. These two claims are the same, because associating the energy with just the electron is saying that the electron on its own can have potential energy. Which it can't.

From my physics textbook

Which textbook?

From my physics textbook, pg 984:

From: University of Tennessee, Knoxville

As I said, you have to read these sources in context. You're not doing that.

Nobody is disputing the math; that's not the issue. The issue is that it's not "a matter of semantics" what the energy is associated with. It has to be associated with the system--in this case the atom--not just the electron. The quotes you give do not contradict that; they are just being sloppy: because they are using a frame in which the proton is at rest, they are describing the PE as though it belonged to the electron, even though it doesn't. But switch frames and this sloppiness no longer works. The actual physics is that the PE is a property of the system, not the electron, regardless of what sloppiness you can get away with in a particular frame.

As for why the actual physics is important, that should be obvious from the discussion in this thread: it explains why the answer to your original question has to be "no".

 

[PeterDonis]

My level of physics has not reached the level where the mass of the electron may change.

It can't--that is precisely @Dale's point. The electron is not a bound system that can even have potential energy on its own. Its mass is a constant and can't change. Advancing your level of understanding won't change that.

 

[Structure seeker]

@avicenna Bohr's theory was meant for electron orbit states around an atom. Imagine a proton without electrons (a H+ ion) absorbing a photon. The proton is moving to the right, the photon to the left. It's simply the law of momentum conservation that the atom will be moving slower after the encounter.

In the case of electrons orbiting an atom moving contrary to an incoming photon: the electron may enter a more excited state, but due to its electronic attraction to the atom core and the gained momentum in contrary direction at first, the atom core will move slightly slower afterwards. The gained energy for the electron is less than the lost kinetic energy of the atom core. The atom's "rest energy" (with the electron still excited) might have increased but its total energy reduced.

 

[Drakkith]

My level of physics has not reached the level where the mass of the electron may change. Give me time to do some catch-up!!!

The mass of the electron doesn't change, and neither does the mass of the nucleus. This is similar to boosting the Moon into a higher orbit around the Earth. Energy has been added, and thus mass, but the mass of the Moon and the Earth don't change. How could they? An observer on the surface of either body would see no physical change in the body, no temperature increase, nowhere that mass or energy has been added. Therefore it must be the mass of the Earth-Moon system as a whole that changes, not the mass of either body.

 

[vanhees71]

I have never ever said that an electron on its own can have potential energy. I only said it is a matter of semantics whether we associate the amount of energy to the electron or to tha atom(the system). The amount is the same!

It is not semantics but a basic misunderstanding. In an atom in an energy eigenstate the electrons and the atomic nucleus are in an entangled state and thus inseparable. You have an energy of the atom as a whole. To talk about distribution of this energy to various parts of the atom doesn't make sense.

Amazingly this is not discussed in the textbooks, although it's an (if not the) important feature of quantum theory. See the following AJP paper

https://arxiv.org/abs/quant-ph/9709052
https://doi.org/10.1119/1.18977

 

[bob012345]

It is not semantics but a basic misunderstanding. In an atom in an energy eigenstate the electrons and the atomic nucleus are in an entangled state and thus inseparable. You have an energy of the atom as a whole. To talk about distribution of this energy to various parts of the atom doesn't make sense.

Amazingly this is not discussed in the textbooks, although it's an (if not the) important feature of quantum theory. See the following AJP paper

https://arxiv.org/abs/quant-ph/9709052
https://doi.org/10.1119/1.18977

Why do you think it's the most important feature of quantum theory?

 

[vanhees71]

If there's one feature which is really "quantum" in contradistinction to "classical physics", it's entanglement, I'd say, but that's of course a pretty subjective opinion.

 

[bob012345]

If there's one feature which is really "quantum" in contradistinction to "classical physics", it's entanglement, I'd say, but that's of course a pretty subjective opinion.

OK, but would there be any difference from using the usual Schrödinger approach by considering the proton and electron as an entangled state vs. the electron in a coulomb potential?

 

[vanhees71]

The usual Schrödinger approach directly leads to this result. The point is to write the Hamiltonian in terms of center-of-mass and relative coordinates. The center-of-mass motion is free, and the relative-coordinate piece leads to the usual hydrogen atom for a quasiparticle around the center (which is the center of mass of electron and proton) with the reduced mass, $\mu=m_{\text{e}} m_{\text{p}}/(m_{\text{e}}+m_{\text{p}})$. It's as in classical mechanics (Kepler problem). While a product state in center-of-mass and relative coordinates, rewritten again in electron and proton observables, it's showing that electron and proton are in an entangled state.

 

[hilbert2]

Maybe it's also possible that some exotic particle in high-energy physics can absorb a photon to become a higher-mass particle without the KE or PE changing?

 

[Dale]

Maybe it's also possible that some exotic particle in high-energy physics can absorb a photon to become a higher-mass particle without the KE or PE changing?

You would need to be clear what you mean by PE not changing in that case. But yes, in principle that could happen.