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 $N_{2}=900$