Question

a.) A photon with kinetic energy equal to the mass energy of an electron scatters from an electron at angle ( pi/2). Find the wavelength of the scattered photon.

b.) A photon with kinetic energy equal to the mass energy of an electron scatters from an electron at angle ( pi ). Find the wavelength of the scattered photon.

Answer 1

Δλ = λnew - λ = (h/mec) (1 - cosθ)
h/mec = 2.43 x 10-12 m

The collision causes the photon wavelength to increase by 1 (for a scattering angle of pi/2 or 90°) and twice the Compton wavelength (for a scattering angle of pi or 180°)

λnew is the new wavelength of photon
λ is the original wavelength of photon.

λ = hc/E,

E = 8.187×10−14 joules (rest mass energy of electron)
hc = 1.986*10−25 Jm
λ = 2.43 x 10-12 m
for pi/2, λnew = 4.86 x 10-12 m
for pi, λnew = 7.29 x 10-12 m