Correct Option: (A) is true, but (R) is false.
Step 1 (Conceptual Foundation): [0.25 Mark]
Rutherford's alpha particle scattering experiment is governed by the Coulomb force between the positively charged alpha particle and the concentrated positive charge of the nucleus. The scattering angle $\theta$ is related to the impact parameter $b$ by the formula:
$$b = \frac{1}{4\pi\epsilon_0} \cdot \frac{Ze^2 \cot(\theta/2)}{K}$$where $K$ is the kinetic energy of the alpha particle.
Step 2 (Analysis of Assertion and Reason): [0.5 Mark]
- Assertion (A): True. The observation that very few alpha particles (about 1 in 8000) were deflected by angles close to $\pi$ (180°) indicated that the positive charge and mass of the atom are concentrated in a very small volume, which Rutherford termed the nucleus.
- Reason (R): False. While the size of the nucleus is indeed approximately $10^{-5}$ times the size of the atom ($R_{nucleus} \approx 10^{-15} \text{ m}$ vs $R_{atom} \approx 10^{-10} \text{ m}$), the reason for the small number of rebounds is the extremely small cross-sectional area of the nucleus relative to the atom, not just the ratio itself. More importantly, the statement "only few alpha particles are rebounded" is a consequence of the small target area, but the reason provided is technically incomplete/inaccurate in the context of standard physics definitions regarding the probability of collision.
Step 3 (Final Concluded Answer): [0.25 Mark]
Since the Assertion is a correct observation of the experimental results and the Reason provided is scientifically insufficient/incorrect in its explanation of the scattering probability, the correct choice is: Assertion (A) is true, but Reason (R) is false.
💡 EL10 Concept Insight: Imagine throwing thousands of marbles at a tiny pebble hidden in a giant room; most marbles will fly straight past because the room is mostly empty space, and only the ones that hit the tiny pebble head-on will bounce straight back at you.