Answer
(a) $20^{0}$
Work Step by Step
in Compton effect least Recoil energy received by the least change in electron means least change in wavelength $\Delta\lambda$
$\Delta\lambda = \lambda-\lambda_{0} = \lambda_{c}(1-cos\theta)$
where $\lambda_{c}$ is compton wavelength and $\theta$ is scattering angle .
investigating with given values of $\theta$, $\Delta\lambda$ is least with
$\theta$ = $20^{0}$ ,
{
$\theta$ = $20^{0}$ , $\Delta\lambda= \lambda_{c}(1-cos 20^{0})$=$\lambda_{c}(1-0.93)$= 0.07$\lambda_{c}$
$\theta$ = $45^{0}$ , $\Delta\lambda= \lambda_{c}(1-cos 45^{0})$=$\lambda_{c}(1-0.707)$= 0.293$\lambda_{c}$
$\theta$ = $60^{0}$ , $\Delta\lambda= \lambda_{c}(1-cos 60^{0})$=$\lambda_{c}(1-0.5)$= 0.5$\lambda_{c}$
$\theta$ = $80^{0}$ , $\Delta\lambda= \lambda_{c}(1-cos 80^{0})$=$\lambda_{c}(1-0.173)$= 0.827$\lambda_{c}$
}
