Question

X-rays of wavelength 22 pm are scattered from a carbon target at an angle of 85° to the incident beam. The Compton shift for X-rays is​

Answer 1

Compton shift happens when strong beam of gamma or x rays are incident on a material like carbon, and transfer some energy & momentum to electrons in that.  Some energy in photons in the rays are lost.  The collision is inelastic.

Then the photon is scattered with increased wavelength.  
λ' - λ = shift =  h (1  - cosθ) / (m_e c) = 2.43 (1 - Cosθ) pm
    = 2.43 (1 - Cos 83) = 2.133  pm
The wavelength of weakened x rays = 22+2.133 pm