Compton effect
You scatter x-rays of wavelength 0.0119 nm from the loosely bound electrons of a target material. Find the angle at which the wavelength of the scattered x-rays is longer than the incident wavelength by a factor of f = 1.0339.
Scattering on loosely bound electrons means this is Compton scattering.
The relation of wavelength for Compton scattering is
$\lambda2- \lambda1 = [h/(m*c)]*[1-cos(\theta)]$
$\lambda2 = 1.0339*\lambda1$
$(0.0339*\lambda1*m*c)/h =1-cos(\theta)$
$\lambda1 =0.0119 nm$
$m =9.1*10^{-31} kg$
$h =6.626*10^{-34}$
$1-cos(\theta) =0.16621$
$\theta =33.5 degree$