Energy transfer from photon to an electron

[Jimmy Moriaty]

Please tell me,why can't a photon transfer it's energy completely to a free electron?

 

[Orodruin]

This would necessarily violate the conservation of momentum.

 

[Drakkith]

So what happens when the electron absorbs the photon?

 

[Jimmy Moriaty]

This would necessarily violate the conservation of momentum.

This would necessarily violate the conservation of momentum.

But in the photo-electric effect it's happeing.why?

 

[Orodruin]

But in the photo-electric effect it's happeing.why?

Momentum is being transferred to something else and therefore it is conserved overall.

 

[Jimmy Moriaty]

So what happens when the electron absorbs the photon?

Then,why can't electron travel the same direction which the photon have been travelled?
(after absorbing the energy of photon)

Momentum is being transferred to something else and therefore it is conserved overall.

Then, why can't electron travel the same direction which the photon have been travelled?(after absorbing the energy of photon)

 

[Drakkith]

Then,why can't electron travel the same direction which the photon have been travelled?
(after absorbing the energy of photon)

Don't ask me, that's what I want to know!

 

[Orodruin]

Then,why can't electron travel the same direction which the photon have been travelled?
(after absorbing the energy of photon)

Then, why can't electron travel the same direction which the photon have been travelled?(after absorbing the energy of photon)

It can, as long as there is something else involved to ensure momentum conservation. If the electron is free, it simply cannot absorb a photon due to momentum conservation.

 

[Nugatory]

Then, why can't electron travel the same direction which the photon have been travelled?(after absorbing the energy of photon)

Try it... The electron changes its speed from 0 to $v$ as it absorbs the photon. The kinetic energy of the (non-relativistic, for simplicity) electron increases from zero to $mv^2/2$ and the momentum from 0 to $mv$. If the photon is to be completely absorbed and energy and momentum are to be conserved, then these values must be equal to the energy $p_{\gamma}c$ and the momentum $p_{\gamma}$ of the initial photon. A bit of algebra will pretty quickly convince you that this isn't possible - if the increase in the electron's energy is equal to the photon's total energy then the momentum won't balance, and vice versa.

 

[Jimmy Moriaty]

Try it... The electron changes its speed from 0 to $v$ as it absorbs the photon. The kinetic energy of the (non-relativistic, for simplicity) electron increases from zero to $mv^2/2$ and the momentum from 0 to $mv$. If the photon is to be completely absorbed and energy and momentum are to be conserved, then these values must be equal to the energy $p_{\gamma}c$ and the momentum $p_{\gamma}$ of the initial photon. A bit of algebra will pretty quickly convince you that this isn't possible - if the increase in the electron's energy is equal to the photon's total energy then the momentum won't balance, and vice versa.

Yeah!
You are right.There is a difference between those two velocities.
I've chose the wavelength of 0.071nm x-rays.
When I consider the E=Pc & P=mv I've got v=1.025*10^7 ms^-1
But when i chose E=Pc & E=1/2 mv^2 it's v=7.84*10^7 ms^-1
But what's the reason for this?

 

[Nugatory]

But what's the wrong in this assumption?

You're assuming that there is a way for a photon to transfer all its energy and momentum to a single particle while respecting the laws of mechanics. The math exercise is showing that making this assumption inevitably leads to a contradiction.

 

[Dale]

But what's the reason for this?

The reason is that the mass of the electron is fixed. If the electron could become more massive then it would be possible to conserve both the energy and the momentum of the collision. This is why a free atom can absorb a photon but not a free electron.

 

[Drakkith]

So what happens? Does the free electron interact with the photon at all?

 

[Dale]

Yes. It scatters. So an electron and a photon come in, and an electron and a photon come out.

 

[Drakkith]

Ah, okay. Thanks, Dale.

 

[blue_leaf77]

I've chose the wavelength of 0.071nm x-rays.
When I consider the E=Pc & P=mv I've got v=1.025*10^7 ms^-1
But when i chose E=Pc & E=1/2 mv^2 it's v=7.84*10^7 ms^-1
But what's the reason for this?

That's quite relativistic values. Just for an advice for a more accurate verification is to use relativistic formula, upon which you should find that $\hbar \omega + m_ec^2 = \sqrt{(\hbar \omega)^2 + (m_ec^2)^2}$ and you see the discrepancy very clearly. As Dale has said, this equation can be satisfied if $m_e$ on the RHS is allowed to increase.

 

[ZapperZ]

But in the photo-electric effect it's happeing.why?

This really needs to be clarified and corrected.

In the photoelectric effect, and in photoionization, the interaction is NOT with "free electrons". The electrons are either coupled to the lattice solid (as in the photoelectric effect) or bound in an atom. So your question about "free electron" and then asking about photoelectric effect is really comparing apples with oranges. It is not the same thing.

When photons hit either a metal or an atom, it is the whole solid or the whole atom that interacts. The energy bands and the energy levels that the electrons get promoted to are not present in free electrons. That is why the solid or the atom are the ones that are in the excited state. A consequence of this is that one or more electrons change state to a higher energy state. So while it is tempting to focus on just the electrons, since they are the ones that were changed, it is the entire solid or the entire atom that actually is responsible to allow for the energy absorption from the photons.

Zz.

 

[Jimmy Moriaty]

Thank you everyone!

 

[drl]

If a photon can give a packet of energy to an electron, overcoming its work function and freeing it up, can a low energy photon recover that same packet and cause the electron to revert to its bound state? I am assuming that an electron and an atom exist in particle form in their bound state and in a wave form in their free state.

 

[Drakkith]

If a photon can give a packet of energy to an electron, overcoming its work function and freeing it up, can a low energy photon recover that same packet and cause the electron to revert to its bound state?

Not sure. That almost sounds like stimulated emission, but that process doesn't involve light of different wavelengths.

I am assuming that an electron and an atom exist in particle form in their bound state and in a wave form in their free state.

That would be incorrect. There aren't two separate states that objects transition between. They always behave according to their fundamental properties, some of which are 'wave-like' and some of which are 'particle-like'.

 

[drl]

Bohr said that they can only exist separately and what I've read most physicists seem to agree.

 

[Drakkith]

Bohr said that they can only exist separately and what I've read most physicists seem to agree.

What exists separately?

 

[drl]

Not sure. That almost sounds like stimulated emission, but that process doesn't involve light of different wavelengths.
That would be incorrect. There aren't two separate states that objects transition between. They always behave according to their fundamental properties, some of which are 'wave-like' and some of which are 'particle-like'.

 

[Nugatory]

Bohr said that they can only exist separately and what I've read most physicists seem to agree.

You've been victimized by the pop-sci explanations of quantum mechanics. Bohr actually said something subtly different: you can design and execute experiments that show wave-like behavior, and you can design and execute experiments that show particle-like behavior, but you cannot design a single experiment that shows both at the same time.

 

[drl]

I believe that Bohr said that that wave and particle form cannot exist at the same time.The reason I asked about the exchange of energy between the electron (in its free or wave state ) and a low energy photon recovering the energy packet which overcame the electromagnetic attraction to an atom (work function) this would return the electron to its bound particle form from its free wave form. Add to this the assumption that when light,electrons or atoms approach the 2 slits they are in their free wave forms or they would still be in a bound particle state.i.e. when a particle leaves its bound state it is converted to a free wave state. Got it? The ability to revert back and forth as a result of transfer of energy packet equivalent to the work function could solve a lot of problems in the 2 slit experiment. Appreciate any further comments and thax for your interest.

 

[Drakkith]

I believe that Bohr said that that wave and particle form cannot exist at the same time.The reason I asked about the exchange of energy between the electron (in its free or wave state ) and a low energy photon recovering the energy packet which overcame the electromagnetic attraction to an atom (work function) this would return the electron to its bound particle form from its free wave form.

Electrons don't exist in 'particle form' while bound to an atom. They don't even have a single, well-define position. They exist in an orbital, which is a probability map of where it is likely to be. This is also true for the protons and neutrons, along with the quarks and gluons that compose nucleons.

Add to this the assumption that when light,electrons or atoms approach the 2 slits they are in their free wave forms or they would still be in a bound particle state.i.e. when a particle leaves its bound state it is converted to a free wave state. Got it? The ability to revert back and forth as a result of transfer of energy packet equivalent to the work function could solve a lot of problems in the 2 slit experiment.

I'm sorry but this simply isn't how it works.