In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot ?
Answer: (C) see figure
Concept. Rutherford's scattering formula gives the number of $\alpha$-particles scattered at angle $\theta$:
$$N(\theta) \propto \frac{1}{\sin^4(\theta/2)}$$
Step 1. Small angles. Most $\alpha$-particles pass almost undeflected, so $N(\theta)$ is very large near $\theta = 0$.
Step 2. Large angles. As $\theta$ grows, $\sin(\theta/2)$ grows and $N$ falls very steeply; only a few particles come back near $\theta = 180°$.
Step 3. Choose the graph. The correct plot falls steadily and sharply with $\theta$, which is graph (3).
Answer. Graph (3) (Option C).
Solution by Sreeraj P, M.Sc Physics