Question

In Rutherford experiment a-particles are scattered by nucleus having charge 100 e. Initial kinetic energy of a-particles is 6 MeV. The size of the nucleus is–

• A. 10^–14 m
• B. 5 × 10^–14 m
• C. 10^–13 m
• D. 10^–16 m

Answer 1

Answer: (B)

5 × 10^–14 m

Answer 2

A rough estimate of size of the nucleus is given by the distance of closest approach of an

a-particle incident head-on on a nucleus of charge Ze;

K = $\frac{1}{2}$ mv² = $\frac{2Ze^{2}}{4\pi\varepsilon_{0}d}$» $\frac{2Ze^{2}}{4\pi\varepsilon_{0}r}$

[where K = 6

Z =10]

r = $\frac{2 \times 100 \times (1.6 \times 10^{- 19})^{2} \times 9 \times 10^{9}}{6 \times 10^{6} \times 1.6 \times 10^{- 19}}$

r = 5 × 10^–14 m