During Compton scattering, a grazing collision occurs between an x-ray photon (p
ID: 1306461 • Letter: D
Question
During Compton scattering, a grazing collision occurs between an x-ray photon (p+) and a stationary electron (e-). A deflected outgoing p+ is detected which has a longer wavelength than the incoming p+. This difference is explained by the fact that the e- has to recoil and absorb some of the energy of the incoming p+. The interaction can be modeled by the following rxn:
incoming photon + stationary electron --> outgoing photon + moving electron
In a specific trial, the photon's wavelenth is measured to change from 7.078 x 10^-2 nm to 7.314 x 10^-2 nm. Using conservation of energy, determine the moving electron's velocity and wavelength.
a. What are the energies of the incoming and outgoing photons?
b. What is the final kinetic energy of the electron?
c. What are the velocity and wavelength of the moving electron?
Explanation / Answer
a) Ein = h*c/lamda_in
= 6.626*10^-34*3*10^8/7.078*10^-7
= 2.808*10^-19 J
= 1.755 eV
Eout = h*c/lamda_out
= 6.626*10^-34*3*10^8/7.314*10^-7
= 2.7178*10^-19 J
= 1.6986 eV
b) KE = Ein - Eout = 0.05637 eV = 9*10^-21 J
c) KE = 0.5*m*v^2
v = sqrt(2*Ke/m)
= sqrt(2*9*10^-21/9.1*10^-31)
= 1.406*10^5 m/s
lamda = h/(m*v)]
= 6.626*10^-34/(9.1*10^-31*1.406*10^5)
= 5.178*10^-9 m
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