Explanation

(a) According to scattering formula
$N \propto \frac{1}{\sin^{4}(\theta/2)} \Rightarrow \frac{N_{2}}{N_{1}} = \left\lbrack \frac{\sin{(\theta_{1}/2)}}{\sin{(\theta_{2}/2)}} \right\rbrack^{4}$
$\Rightarrow \frac{N_{2}}{N_{1}} = \left\lbrack \frac{\sin\frac{90{^\circ}}{2}}{\sin\frac{60{^\circ}}{2}} \right\rbrack^{4} = \left\lbrack \frac{\sin{45{^\circ}}}{\sin{30{^\circ}}} \right\rbrack^{4}$
$\Rightarrow N_{2} = \left( \sqrt{2} \right)^{4} \times N_{1} = 4 \times 56 = 224$