a
(a) According to scattering formula

\(N \propto \frac{1}{{{{\sin }^4}(\theta /2)}} \Rightarrow \frac{{{N_2}}}{{{N_1}}} = {\left[ {\frac{{\sin ({\theta _1}/2)}}{{\sin ({\theta _2}/2)}}} \right]^4}\)

\( \Rightarrow \frac{{{N_2}}}{{{N_1}}} = {\left[ {\frac{{\sin \frac{{{{90}^o}}}{2}}}{{\sin \frac{{{{60}^o}}}{2}}}} \right]^4} = {\left[ {\frac{{\sin {{45}^o}}}{{\sin {{30}^o}}}} \right]^4}\)

\( \Rightarrow {N_2} = {(\sqrt 2 )^4} \times {N_1} = 4 \times 56 = 224\)