Question Analysis: Assertion (A) and Reason (R) type question.
Step 1 (Formula / Governing Law): [0.5 Mark]
The relationship between the impact parameter ($b$) and the scattering angle ($\theta$) in Rutherford alpha-particle scattering is given by the formula:
$$b = \frac{1}{4\pi\epsilon_0} \cdot \frac{Ze^2 \cot(\theta/2)}{K.E.}$$Where $Z$ is the atomic number of the target nucleus, $e$ is the elementary charge, and $K.E.$ is the kinetic energy of the alpha particle.
Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]
- For Assertion (A): When $\theta = 180^{\circ}$, then $\theta/2 = 90^{\circ}$. Since $\cot(90^{\circ}) = 0$, the impact parameter $b$ becomes $0$. Thus, the impact parameter is minimum (not maximum) for a scattering angle of $180^{\circ}$. Therefore, Assertion (A) is False.
- For Reason (R): From the formula $b \propto Z$, it is evident that the impact parameter depends directly on the atomic number ($Z$) of the target nucleus. Therefore, Reason (R) is False.
Step 3 (Final Concluded Answer): [0.25 Mark]
Correct Option: (d) Both Assertion (A) and Reason (R) are false statements.
💡 EL10 Concept Insight:
Think of the impact parameter as the "aim" of the alpha particle; if you aim directly at the center of the nucleus (impact parameter = 0), the particle bounces straight back ($180^{\circ}$), so the scattering angle is largest when the impact parameter is smallest! Also, a heavier nucleus (higher $Z$) has a stronger electric push, so it deflects particles more easily, meaning the impact parameter definitely depends on the target's atomic number.