A) 224
B) 256
C) 98
D) 108
Correct Answer: A
Solution :
According to scattering formula \[N\propto \frac{1}{{{\sin }^{4}}(\theta /2)}\Rightarrow \frac{{{N}_{2}}}{{{N}_{1}}}={{\left[ \frac{\sin ({{\theta }_{1}}/2)}{\sin ({{\theta }_{2}}/2)} \right]}^{4}}\] \[\Rightarrow \frac{{{N}_{2}}}{{{N}_{1}}}={{\left[ \frac{\sin \frac{{{90}^{o}}}{2}}{\sin \frac{{{60}^{o}}}{2}} \right]}^{4}}={{\left[ \frac{\sin {{45}^{o}}}{\sin {{30}^{o}}} \right]}^{4}}\] \[\Rightarrow {{N}_{2}}={{(\sqrt{2})}^{4}}\times {{N}_{1}}=4\times 56=224\]
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