In the Geiger–Marsden experiment, the number of scattered α-particles N(θ) is plotted as a function of scattering angle θ. Which option represents the correct plot?

Solution & Explanation

This is the angular distribution of α-particles in the Geiger–Marsden (Rutherford) gold-foil experiment. Rutherford's scattering formula gives the number scattered at angle θ as N(θ) ∝ 1/sin⁴(θ/2). For small θ, sin⁴(θ/2) is tiny, so N(θ) is enormous — the overwhelming majority of α-particles pass nearly straight through, deflected only slightly. As θ increases, sin⁴(θ/2) grows rapidly, so N(θ) falls off very steeply. Only a very few particles are scattered through large angles (this rare large-angle scattering is what revealed the tiny dense nucleus). So the plot is very large at small θ and decreases sharply with increasing θ. This matches answer (C): N(θ) very large at small θ, falling steeply as θ increases.