X-rays of wavelength 0.2 nm are scattered from a block of carbon. If t

1.	X-rays of wavelength 0.2 nm are scattered from a block of carbon. If the scattered radiation is detected at 90◦to theincident beam, find (a) the Compton shift, and (b) the kinetic energy imparted to the recoiling electron.
Answer» 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 m_e = mass of electron λ_f - λ_i\(=\frac h{m_ec}\) (1 - cos θ) (θ = 90°, cos 90° = 0) λ_f - 0.2 x 10^-9 \(=\frac h{m_ec}\) λ_f - 0.2 x 10^-9 \(=\frac{6.63\times10^{-34}}{9.1\times10^{-31}\times3\times10^8}\) λ_f= 0.2 x 10^-9 + 0.24 x 10^-11 λ_f = 0.20 x 10^-10 + 0.024 x 10^-10 λ_f= 0.224 x 10^-10 λ_f = 0.0224 x 10^-9 m Compton shift Δλ = λ_f - λ_i Δλ = 0.0224 - 0.2 Δλ = -0.1776 nm (b) Kinetic energy imparted to the recoiling electron. E_k \(=\frac{h^2}{2m\lambda^2}\) E_k \(=\frac{(6.64\times10^{-34})^2}{2\times9.1\times10^{-31}\times(0.2\times10^{-9})^2}\) E_k \(=\frac{44.08\times10^{-68}}{0.728\times10^{-18}\times10^{-31}}\) E_k= 60.54 x 10^-19 J K.E = 37.83 eV

X-rays of wavelength 0.2 nm are scattered from a block of carbon. If the scattered radiation is detected at 90◦to theincident beam, find (a) the Compton shift, and (b) the kinetic energy imparted to the recoiling electron.

Answer»

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

m_e = mass of electron

λ_f - λ_i\(=\frac h{m_ec}\) (1 - cos θ) (θ = 90°, cos 90° = 0)

λ_f - 0.2 x 10^-9 \(=\frac h{m_ec}\)

λ_f - 0.2 x 10^-9 \(=\frac{6.63\times10^{-34}}{9.1\times10^{-31}\times3\times10^8}\)

λ_f= 0.2 x 10^-9 + 0.24 x 10^-11

λ_f = 0.20 x 10^-10 + 0.024 x 10^-10

λ_f= 0.224 x 10^-10

λ_f = 0.0224 x 10^-9 m

Compton shift Δλ = λ_f - λ_i

Δλ = 0.0224 - 0.2

Δλ = -0.1776 nm

(b) Kinetic energy imparted to the recoiling electron.

E_k \(=\frac{h^2}{2m\lambda^2}\)

E_k \(=\frac{(6.64\times10^{-34})^2}{2\times9.1\times10^{-31}\times(0.2\times10^{-9})^2}\)

E_k \(=\frac{44.08\times10^{-68}}{0.728\times10^{-18}\times10^{-31}}\)

E_k= 60.54 x 10^-19 J

K.E = 37.83 eV