I would like to know, please, regarding the photoelectric effect and the Compton effect, why is the following process dynamically impossible. I would like to know how to justify by words and also if there is some kind of mathematical demonstration. gamma+e^- => e^-

Valery Cook

Valery Cook

Answered question

2022-10-14

I would like to know, please, regarding the photoelectric effect and the Compton effect, why is the following process dynamically impossible. I would like to know how to justify by words and also if there is some kind of mathematical demonstration.
γ + e e

Answer & Explanation

Phoebe Medina

Phoebe Medina

Beginner2022-10-15Added 17 answers

You cannot simultaneously conserve momentum and energy.
The "reaction" must take place in a straight line. Consider the reaction in the initial rest frame of the electron. Conservation of momentum says that
p γ = p e ,
where p e is the momentum of the electron afterwards.
Conservation of energy says
p γ c + m c 2 = ( p e 2 c 2 + m 2 c 4 ) 1 / 2
But using the first equation this means
p e 2 c 2 + m 2 c 4 + 2 p e m c 3 = p e 2 c 2 + m 2 c 4
This can only be true if the momentum of the electron after the interaction p e = 0 and thus that the initial photon had zero momentum.
Any finite momentum for the initial photon and energy and momentum cannot be conserved.
In the photoelectric effect this problem is solved by transferring some momentum to the remaining ion. In the Compton effect, a lower energy photon appears after the interaction.

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