JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Modern Physics

In Rutherford's scattering experiment the number of $\alpha$-particles detected at angle $\theta$ follows $N\propto 1/{\sin }^4(\theta /2)$. This makes $N$ enormous for small deflections, falls off steeply as $\theta$ grows, and leaves only a tiny count near $\theta =180^{\circ }$. The curve that matches is a sharp peak at small angles decaying rapidly as the angle increases, the hallmark of the ${\sin }^{-4}(\theta /2)$ dependence.