Proving that a free electron can't fully absorb a photon

In summary, the conversation discusses the process of proving that a free, stationary electron cannot fully absorb a photon. The conservation of energy and momentum are two laws that must be fulfilled in this process, and the conversation goes on to discuss how these laws are used to determine the total energy and momentum of the photon and electron. Through this discussion, the individual is able to come to a solution to the problem.
  • #1
squareroot
76
0

Homework Statement


Prove that a free, stationary, electron can't fully absorb a photon

Homework Equations





The Attempt at a Solution


I have no idea where to start.I must mention that i m on the 12 grade and not using calculus-based physics.And I've only studied and learned equations in quantum mechanics that involve Planck's constant(h) and not the reduced Planck constant (h bar).

Thank you!
 
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  • #2
There are two conservation laws to be fulfilled when the electron absorbs the photon. What are they? Can be both of them true?

ehild
 
  • #3
You're talking about the conservation of energy and the conservation of momentum.I presented this solution to my teacher and he rejected it.

Energy of the photon :Ef=pfc
Energy of the electron Ee=mec2

Now, the conservation of energy tells us that the final energy(after the absorbtion) is the same with the energy of the photon and the electron, so:

The total energy E=Ee + Ef

Am I right so far?Because this is the point at which i lose confidence

What's the total energy?
And where do I use the conservation of momentum?

Ty
 
  • #5
squareroot said:
You're talking about the conservation of energy and the conservation of momentum.I presented this solution to my teacher and he rejected it.

Energy of the photon :Ef=pfc
Energy of the electron Ee=mec2

Now, the conservation of energy tells us that the final energy(after the absorbtion) is the same with the energy of the photon and the electron, so:

The total energy E=Ee + Ef

Am I right so far?Because this is the point at which i lose confidence

What's the total energy?
And where do I use the conservation of momentum?

Ty
The electron is in rest initially.
I think you can assume that the speed of the electron would be much below the speed of light, so you can say that the energy of the photon becomes the kinetic energy of the electron, and the momentum of the photon should be equal to the momentum of the electron after their interaction.
You can use he classical formula for the kinetic energy and the momentum of the electron. What are they?
What are the energy and momentum of the photon?


ehild
 
  • #6
I solved it!

Thank you very much!
 
  • #7
You are welcome:smile:

ehild
 

1. How do we know that a free electron can't fully absorb a photon?

Through experiments and observations, scientists have found that when a photon is absorbed by a free electron, the electron can only gain a certain amount of energy. This indicates that the electron did not fully absorb the photon.

2. What evidence supports the idea that a free electron can't fully absorb a photon?

One key piece of evidence is the conservation of energy. If a free electron were able to fully absorb a photon, it would gain an infinite amount of energy, which is not possible according to the laws of thermodynamics. Additionally, experiments have shown that the energy gained by an electron upon absorbing a photon is always less than the energy of the photon itself.

3. Why can't a free electron fully absorb a photon?

Electrons have discrete energy levels, meaning they can only exist at specific energy levels and cannot have any amount of energy in between. When a photon is absorbed, it can only transfer a specific amount of energy to the electron that corresponds to one of these energy levels. This prevents the electron from fully absorbing the photon.

4. Is there any circumstance in which a free electron can fully absorb a photon?

No, there is no known circumstance in which a free electron can fully absorb a photon. However, in certain materials with specific energy band structures, electrons can absorb photons and jump to higher energy levels, giving the appearance of full absorption. But in reality, the electron is still not fully absorbing the photon.

5. How does the inability of a free electron to fully absorb a photon impact our understanding of the photoelectric effect?

The photoelectric effect, in which electrons are ejected from a material when it is exposed to light, is a phenomenon that cannot be fully explained by classical physics. The concept that a free electron cannot fully absorb a photon helps to explain why only certain frequencies of light can cause the ejection of electrons and why there is a threshold frequency. This has led to the development of quantum mechanics, which provides a more complete understanding of the photoelectric effect.

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