Question

A nucleous disintegrates into two nuclear parts which have their velocities in the ratio 2 : 1 .The ratio of their nuclear sizes will be

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

Answer 1

Answer: (C)

$1:2^{\frac{1}{3}}$

Given : $v_1:v_2=2:1$
From conservation of linear momentum, $m_1{v}_1=m_2{v}_2$
$\therefore$ $\frac{m_1}{m_2}=\frac{v_2}{v_1}=\frac{1}{2}$
Mass of nucleus $m\propto A$ where $A$ is the mass number
Nuclear size $R\propto A^{1/3}\propto m^{1/3}$
Thus $\frac{R_1}{R_2}=(\frac{m_1}{m_2}{)}^{1/3}=(\frac{1}{2}{)}^{1/3}$