Physics - Modern Physics Question with Solution | TestHub

In the Geiger-Marsden ($\alpha$-particle scattering) experiment, the number of $\alpha$-particles scattered at an angle $\theta$ is given by the Rutherford scattering formula:

$N(\theta )\propto \frac{1}{{\sin }^4(\theta /2)}$

From this relation, we can observe the following:
1. For small values of $\theta$, $\sin (\theta /2)$ is very small, making $N(\theta )$ very large. Most $\alpha$-particles pass through with very little deflection.
2. As the scattering angle $\theta$ increases, $\sin (\theta /2)$ increases, causing the number of scattered particles $N(\theta )$ to decrease rapidly.
3. The minimum number of scattered particles occurs at $\theta =180^{\circ }$, where $\sin (180^{\circ }/2)=\sin (90^{\circ })=1$.

The graph that correctly represents this rapid decrease from a very high value at small angles to a low value at large angles is shown in option (4).

Answer: