A nucleus disintegrates into two nuclear parts having velocities in the ratio of \( 2:1 \). The ratio of the sizes of their nuclei will be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 1:2^{1/3} \)
The nucleus is initially at rest, so by conservation of momentum the two parts fly apart with equal and opposite momenta:
\( m_{1}v_{1} = m_{2}v_{2} \)
\( \displaystyle \frac{m_{1}}{m_{2}} = \frac{v_{2}}{v_{1}} = \frac{1}{2} \)
The mass of a nucleus is proportional to its mass number \( A \), and the nuclear radius is \( R = R_{0}A^{1/3} \):
\( \displaystyle \frac{R_{1}}{R_{2}} = \left(\frac{A_{1}}{A_{2}}\right)^{1/3} = \left(\frac{1}{2}\right)^{1/3} \)
\( R_{1}:R_{2} = 1:2^{1/3} \)