Question

A nucleus splits into two nuclear parts which have their velocity ratio equal to $2:1$. What will be the ratio of their nuclear radius

• A. $2^{1/3}:1$
• B. ${1:2}^{1/3}$
• C. $3^{1/2}:1$
• D. ${1:3}^{1/2}$

Answer 1

Answer: (B)

${1:2}^{1/3}$

As momentum is conserved, therefore,
$\frac{m_1}{m_2}=\frac{A_1}{A_2}=\frac{v_1}{v_2}=\frac{1}{2}$
$\therefore \frac{R_1}{R_2}={\left(\frac{A_1}{A_2}\right)}^{1/3}={\left(\frac{1}{2}\right)}^{1/3}=1:2^{1/3}$