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daselocution
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Homework Statement
Assume that the total energy E of an electron greatly exceeds its rest energy E0. If a photon has a wavelength equal to the de Broglie wavelength of the electron, what is the photon’s energy? Repeat the prob- lem assuming E = 2E0 for the electron.
I need help with the first part of the problem--I included my answer to the second part in case it is relevant to the first.
Homework Equations
de Broglie wavelength λ=h/p
E^2 = p^2c^2 + m^2c^4
E=hf=hc/λ
The Attempt at a Solution
Part one of the problem:
Knowing that E>>Erest, I can use the mass-energy relation to show that E^2 = P^2c^2, such that E=pc. From this I know that p=E/c
I used this to show that the energy of the photon must be equal to the energy of the electron as follows:
λelectron = λphoton
λelectron = h/p = h/(E/c) = hc/Eelectron
λphoton = hc/Ephoton
hc/Eelectron = hc/Ephoton ---> Eelectron = Ephoton
From here all I can see is that there is an infinite number of solutions. I don't understand how to winnow my process down so that it yields only one solution. That said, I don't even know if my process is 100% correct.
Part two of the problem:
λ=h/pelectron=hc/Ephoton
Ephoton=c/pelectron
E^2 = p^2c^2 + E0^2 = (2Eo)^2 = 4Eo^2
3Eo^2 = p^2c^c
p=√3 * (Eo)/c
such that:
Ephoton=c/pelectron = c/(√3 * (Eo)/c), all of which are constants that I know the values of and which give me a real answer.
What say you all about the first part of the problem?