A nucleus disintegrates into two nuclear fragments which move apart, having their velocities in the ratio 1:3. The ratio of their nuclear sizes, respectively, will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sqrt[3]{3} : 1 \)
The nucleus was at rest, so momentum is conserved and the two fragments carry equal and opposite momenta. The mass of a nucleus is proportional to its mass number \( A \), and its radius follows \( R = R_0 A^{1/3} \).
\( \displaystyle m_1 v_1 = m_2 v_2 \;\Rightarrow\; \frac{m_1}{m_2} = \frac{v_2}{v_1} = \frac{3}{1} \)
\( \displaystyle \frac{A_1}{A_2} = \frac{m_1}{m_2} = 3 \)
\( \displaystyle \frac{R_1}{R_2} = \left(\frac{A_1}{A_2}\right)^{1/3} = 3^{1/3} = \sqrt[3]{3} : 1 \)
The slower fragment is the heavier one, so it has the larger radius.