Question

If number of scattering particles are 56 for ${90}^{\circ }$ angle then the number of scattering particles at ${60}^{\circ }$ angle will be

• A. 224
• B. 256
• C. 98
• D. 108

Answer 1

The correct option is A 224

Using Scattering formula
$N\propto \frac{1}{si{n}^4\left(\frac{\theta }{2}\right)}\Rightarrow \frac{N_2}{N_1}={\left[\frac{sin\left(\frac{{\theta }_1}{2}\right)}{sin\left(\frac{{\theta }_2}{2}\right)}\right]}^4\Rightarrow \frac{N_2}{N_1}={\left[\frac{sin\left(\frac{{90}^{\circ }}{2}\right)}{sin\left(\frac{{60}^{\circ }}{2}\right)}\right]}^4={\left[\frac{sin{45}^{\circ }}{sin{30}^{\circ }}\right]}^4=4\Rightarrow N_2=4N_1=4\times 56=224$