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  4. In Rutherford's experiment, number of particles scattered at 90° angle are x per second. Number particles scattered per second at angle 60° is

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Q. In Rutherford's experiment, number of particles scattered at $90^{\circ}$ angle are $x$ per second. Number particles scattered per second at angle $60^{\circ}$ is

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Solution:

$N(\theta) \propto \frac{Z^{2}}{\sin ^{4}\left(\frac{\theta}{2}\right) E^{2}}$
or $N(\theta) \propto \frac{1}{\sin ^{4}\left(\frac{\theta}{2}\right)}$
$\theta=60^{\circ}$ and $90^{\circ}$
$\therefore \frac{N(90)}{N(60)} \propto \frac{\sin ^{4} 30}{\sin ^{4} 45}$
$N\left(90^{\circ}\right)=x$
$N\left(60^{\circ}\right)=4 x$