Question

A nucleus at rest splits into two nuclear parts having mass number in the ratio $1:2$. Their velocities are in the ratio

• A. $8:1$
• B. $6:1$
• C. $4:1$
• D. $2:1$

Answer 1

The correct option is D $2:1$

As the nucleus is initially at rest, by the conservation of momentum,

$0=m_1{v}_1+m_2{v}_2$

$\Rightarrow \left|\frac{v_1}{v_2}\right|=\frac{m_2}{m_1}$

We know that, $m=\rho \times \text{Volume}$

$\Rightarrow \frac{v_1}{v_2}=\frac{\rho \times \frac{4}{3}\pi R_2^3}{\rho \times \frac{4}{3}\pi R_1^3}=\frac{R_2^3}{R_1^3}.....\left(1\right)$

As, $R=R_0(A{)}^{\frac{1}{3}}$

$\Rightarrow R\propto A^{\frac{1}{3}}.....\left(2\right)$

Using $\left(1\right)$ and $\left(2\right)$,

$\Rightarrow \frac{v_1}{v_2}=\frac{A_2}{A_1}=\frac{2}{1}$

Hence, option $\left(D\right)$ is correct.