Given θ = 90°
(a) Compton effect scattered wavelength incident wavelength compton shift
Δλ \(=\frac h{m_ec}\) (1 - cos θ)
Δλ \(=\frac h{m_ec}\) (1 - cos 90°)
Δλ \(=\frac h{m_ec}\) (1 - 0)
Δλ \(=\frac h{m_ec}\)
where h = plank constant
c = speed of light
me = mass of electron
λf - λi \(=\frac h{m_ec}\) (1 - cos θ) (θ = 90°, cos 90° = 0)
λf - 0.2 x 10-9 \(=\frac h{m_ec}\)
λf - 0.2 x 10-9 \(=\frac{6.63\times10^{-34}}{9.1\times10^{-31}\times3\times10^8}\)
λf = 0.2 x 10-9 + 0.24 x 10-11
λf = 0.20 x 10-10 + 0.024 x 10-10
λf = 0.224 x 10-10
λf = 0.0224 x 10-9 m
Compton shift Δλ = λf - λi
Δλ = 0.0224 - 0.2
Δλ = -0.1776 nm
(b) Kinetic energy imparted to the recoiling electron.
Ek \(=\frac{h^2}{2m\lambda^2}\)
Ek \(=\frac{(6.64\times10^{-34})^2}{2\times9.1\times10^{-31}\times(0.2\times10^{-9})^2}\)
Ek \(=\frac{44.08\times10^{-68}}{0.728\times10^{-18}\times10^{-31}}\)
Ek = 60.54 x 10-19 J
K.E = 37.83 eV