Answer
$\Delta \lambda = 2.65\times 10^{-15}~m$
Work Step by Step
Note that the maximum wavelength shift occurs when the scattering angle is $\phi = 180^{\circ}$
We can find the wavelength shift $\Delta \lambda$:
$\Delta \lambda = \frac{h}{mc}(1-cos~\phi)$
$\Delta \lambda = \frac{h}{mc}(1-cos~180^{\circ})$
$\Delta \lambda = \frac{2h}{mc}$
$\Delta \lambda = \frac{(2)(6.63\times 10^{-34}~J~s)}{(1.67\times 10^{-27}~kg)(3.0\times 10^8~m/s)}$
$\Delta \lambda = 2.65\times 10^{-15}~m$
