CBSE 2025, Set 1

Question

**Assertion (A):** In Rutherford's alpha particle scattering experiment, the presence of only few alpha particles at angle of scattering $\pi$ led him to the discovery of nucleus.

**Reason (R):** The size of nucleus is approximately $10^{-5}$ times the size of an atom and therefore only few alpha particles are rebounded. A). Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A). B). Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A). C). Assertion (A) is true, but Reason (R) is false. D). Both Assertion (A) and Reason (R) are false.

Edvaya · Accepted Answer

The correct answer is Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).. **Assertion (A) — TRUE:** In Rutherford's gold foil experiment (1909–1911), most alpha particles passed through undeflected, but a **very small number** were deflected at large angles, including some at nearly 180° ($\pi$). This observation was unexpected based on Thomson's "plum-pudding" model and led Rutherford to conclude that the positive charge and most of the mass must be concentrated in a tiny, dense **nucleus**. ✓ **Reason (R) — TRUE:** The nucleus has a radius of approximately $10^{-15}$ m, while the atomic radius is approximately $10^{-10}$ m. Therefore: $$\frac{r_{	ext{nucleus}}}{r_{	ext{atom}}} \approx \frac{10^{-15}}{10^{-10}} = 10^{-5}$$ Since the nucleus is only $10^{-5}$ times the size of the atom, the probability of a direct collision (and hence large-angle scattering) is extremely small — only about $10^{-10}$ of the atom's cross-sectional area. This explains why **very few alpha particles** are scattered back. ✓ **R correctly explains A:** The small size of the nucleus (10⁻⁵ times atomic size) directly explains why only a tiny fraction of alpha particles experience large-angle scattering. **Answer: (A) — Both true, R correctly explains A.**

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