The impact parameter for an $α$-particle approaching a target nucleus is minimum when the scattering angle θ is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (π) rad
The impact parameter is the perpendicular distance between the initial velocity vector of the α-particle and the center of the nucleus.
For Rutherford scattering, the relation between impact parameter (b) and scattering angle (θ) is:
$b = \frac{k Z_1 Z_2 e^2}{2E} \cot\frac{\theta}{2}$
From the equation, $b$ is minimum when $\cot\frac{\theta}{2}$ is minimum.
Minimum value of $\cot\frac{\theta}{2}$ occurs when $\theta = 180^\circ$.
Final Answer: $\theta = 180^\circ$