Answer
(a) $1.58\frac{Km}{s}$
(b) $62.4^{\circ}$
Work Step by Step
(a) We know that
$\lambda=\frac{h}{p}=\frac{h}{mv}$
This can be rearranged as:
$v=\frac{h}{m\lambda}$
We plug in the known values to obtain:
$v=\frac{6.63\times 10^{-34}}{1.67\times 10^{-27}\times 0.250\times 10^{-9} }$
$v=1.58\times 10^3\frac{m}{s}=1.58\frac{Km}{s}$
(b) We can find the angle as
$2dsin\theta=2\lambda $
$\implies 2\times 0.282\times 10^{-9}\times sin\theta=2\times 0.250\times 10^{-9}$
$\implies sin\theta=0.886$
$\theta=62.4^{\circ}$
