Aphoton with wavelength λ = 0.0830 nm is incident on an electron that is initially at rest. if the photon scatters in the backward direction, what is the magnitude of the linear momentum of the electron just after the collision with the photon?

Compton scattering equation of wavelengths 
λ'-λ = h/mec (1 - CosФ)
λ' = λ + h/mec (1 - cos 180°)
= ( 0.0830nm) + (6.626 × 10⁻³⁴ J.s)/ (9.1 × 10⁻³¹ kg)(3.0 × 10⁸ m/s
= 0.0830nm
The momentum of electron is
P photon λ = Pe + P phpton λ'
Pe = h/λ - ( -h/λ') = h(λ' + λ)/λλ'
= (6.626 × 10⁻³⁴ J.s)(( 0.08785nm) +( 0.0883nm)/0.08785nm)( 0.083nm)
1.55 × 10⁻²³ kg.m/s.