What is the maximum kinetic energy of electrons knocked out of a thin copper foil by Compston scattering of an incident beam of 17.5 KeV rays? Assume the work function is negligible.
Δλ = h/mc (1-cosθ)
The Attempt at a Solution
I reasoned that the greatest energy transfer to an electron will occur when the x-ray rebounds at 180 degrees, in which case the change in wavelength is 4.85 x 10^-12 m.
I figured that the wavelength of the x-rays increases by this amount, thereby decreasing in energy. I thought I could therefore take this change in wavelength and calculate the energy associated with it using E = hc/Δλ, and I got E = 256 KeV.
However, the answer key requires that you calculate the wavelength of the original x-ray, add Δλ, then calculate the energy and deduct the original energy. It yields a different answer, 1.1 KeV.
I don't understand why you can't say that the energy loss associated with the increase in the wavelength of the x-ray is completely transferred to the electron and then be done with it. What am I missing? Thanks!