In Geiger Marsden alpha scattering experiments, a beam of alpha particles emitted from \( {}^{214}_{83}\mathrm{Bi} \) were directed to strike a gold foil and various observations were made. Now answer the following questions.
The trajectory of alpha particles depends on the impact parameter of the collision. The impact parameter was found to be minimum for the alpha particles, the scattering angle (nearly) is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( \pi \)
The impact parameter \( b \) is the perpendicular distance of the initial velocity of the alpha particle from the centre of the nucleus. The smaller \( b \), the closer the particle passes to the nucleus and the larger the repulsion it feels, so the larger the scattering angle.
\( \displaystyle b \propto \cot\frac{\theta}{2} \)
When \( b \) is minimum (practically zero) the collision is head-on: \( \cot(\theta/2) \to 0 \), so \( \theta/2 \to \pi/2 \) and \( \theta \to \pi \). The alpha particle rebounds back along its path.
NCERT (2026-27):
Alpha-Particle Trajectory – “… It is seen that an α-particle close to the nucleus (small impact parameter) suffers large scattering. In case of head-on collision, the impact parameter is minimum and the α-particle rebounds back (\( \theta \cong \pi \)). For a large impact parameter, the α-particle goes nearly undeviated and has a small deflection (\( \theta \cong 0 \)).”