Question

A photon of wavelength 18.0 pm is scattered through an angle of 120° by a stationary electron. What is the wavelength of the scattered photon? (A) 19.2 pm (B) 20.4 pm (C) 21.6 pm (D) 22.9 pm

Answer 1

(C) 21.6 pm

Step-by-step explanation:

`\lambda_i`= Initial wavelength = 18 pm

`\lambda_f`= Final wavelength

mc² = Eloectron rest mass = 0.511 MeV

h = Planck's constant

c = Speed of light

hc = 1240 eV nm

`\Delta \lambda=\lambda_f-\lambda_i=(hc)/(mc^2)(1-cos\theta)\\\Rightarrow \lambda_f-18=(1240)/(0.511)(1-cos120)\\\Rightarrow \lambda_f-18=3.63\\\Rightarrow \lambda_f=3.63+18\\\Rightarrow \lambda_f=21.63`

∴ Wavelength of the scattered photon is 21.63 pm