Answer
$\frac{\Delta \lambda}{\lambda} = 9.76\times 10^{-2}$
Work Step by Step
We can find the fractional Compton shift
$\frac{\Delta \lambda}{\lambda} = \frac{(h/mc)(1-cos~90^{\circ})}{hc/E}$
$\frac{\Delta \lambda}{\lambda} = \frac{h/mc}{hc/E}$
$\frac{\Delta \lambda}{\lambda} = \frac{E}{mc^2}$
$\frac{\Delta \lambda}{\lambda} = \frac{(50.0\times 10^3~eV)(1.6\times 10^{-19}~J/eV)}{(9.109\times 10^{-31}~kg)(3.0\times 10^8~m/s)^2}$
$\frac{\Delta \lambda}{\lambda} = 9.76\times 10^{-2}$
