Question

14. (a) A photon with initial wavelength of 6.76×10−12 m strikes an electron, and then has a wavelength of 7.02×10−12 m after it is deflected. What is the deflection angle?

(b) A photon with initial wavelength of 7.36×10−12 m strikes an electron. What is the maximum possible wavelength of the deflected photon and what angle does this correspond to?

Answer 1

According to Compton effect,

Δλ = λ^/ - λ = (h/m_ec) (1 - cosθ)= 2.43 × 10^-12×(1- cos)

As h/m_ec = 2.43 x 10^-12 m

a) (7.02-6.76) × 10^-12 = 2.43 × 10^-12 (1-cos)

1-cos = 0.107

Cos = 0.893

= 26.75⁰

b) maximum change in wavelength takes place for deflection angle of 180⁰

Δλ = λ^/ - λ = (h/m_ec) (1 - cosθ)

For = 180⁰

Δλ = λ^/ - λ = (h/m_ec) × 2 = 2× 2.43 x 10^-12 m

λ^/ - 7.36×10^-12 m = 4.86 × 10^-12

λ^/ = 1.222 ×10^-11 m