The impact parameter for an $α$-particle approaching a target nucleus is minimum when the scattering angle θ is

(π) rad

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: $\theta = 180^\circ$