Question

In Rutherford's $\alpha$ -particle experiment with thin gold foil, $8100$ scintillations per minute are observed at an angle of $60^{\circ }.$ The number of scintillations per minute at an angle of $120^{\circ }$ will be

• A. 900
• B. 2025
• C. 32400
• D. 4050

Answer 1

Answer: (A)

Number of $\alpha$ -particles scattered through angle $\theta$
$N\propto \frac{1}{{\sin }^4\left(\frac{\theta }{2}\right)}$
or $\frac{N_1}{N_2}=\frac{\left({\sin }^4\frac{{\theta }_2}{2}\right)}{\left({\sin }^4\frac{{\theta }_1}{2}\right)}$
or $\frac{8100}{N_2}=\frac{\left({\sin }^4\frac{120}{2}\right)}{\left({\sin }^4\frac{60}{2}\right)}$
$\frac{8100}{N_2}=\frac{{\sin }^{4}60}{{\sin }^{4}30}$
$\Rightarrow N_2=\frac{8100\times \frac{1}{16}}{\frac{9}{16}}$
or $N_2=900$