X-ray photons of wavelength .02480 nm are incident on a target and the Compton-s

Question

X-ray photons of wavelength .02480 nm are incident on a target and the Compton-scattered photons are observed at 90 degrees. (a) What is the wavelength of the scattered photons? (b) What is the momentum of the incident photons? Of the scattered photons? (c) What is the kinetic energy of the scattered electrons? (d) What is the momentum (magnitude and direction) of the scattered electrons? ***I came up with (a) .027226 nm (b) 5*10^4 eV/C __ 4.6*10^4 eV/C (c) 4.5*10^3 eV (d) 4.5*10^3 eV. I do not think the momentum and kinetic energy should have the same value.

Explanation / Answer

The energy of the photon is 8409 eV before and 8336 eV after the scattering. The difference 73 eV is transfered to the electron as kinetic energy. So 73 eV = 0.5 x 0.511 MeV/c^2 x v^2. Therefore (v/c)^2 = 73/(0.5 x 0.511 x 10^6) and v = 0.0154 c = 4530 km/s. The direction is 90 - ?/2 degrees

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