Answer
(a)(2) - Less than 5keV but not zero.
Conservation of momentum and energy is applicable here. Applying the same, electron ought to recoil. Hence, it should ideally possess some amount of kinetic energy in exchange of photon energy.
It does possess some amount of energy, but it is diminished and is less as compared to its initial amount and is not zero.
(b) $20eV$
Work Step by Step
Let, $\theta$ represent "lambda"
Given, $\theta$=$0.25nm$=$2.5\times10^{-10}m$
We know, $ E$=$hF$, where $F$=frequency, $h$ = $6.625\times10^{-34}m^{2}kg/s$, $c=3\times10^{8}m/s$
substituting,
$E$=$\frac{hc}{\theta}$= $\frac{6.625\times10^{-34}\times3\times10^{8}}{2.5\times10^{-10}}$
$E=7.96\times10^{-16}J$
Converting the value to KeV, $\frac{7.96\times10^{-16}}{1.6\times10^{-19}}eV$ = $4.98KeV$
Hence, $KE= 5KeV-4.98KeV = 0.02KeV = 20eV$
