Question 341: Atoms & Nuclei

Question

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be $${\left( {{x \over 3}} \right)^{{1 \over 3}}}$$. The value of '$$x$$' is :-

Accepted Answer

$$
\begin{aligned}
& \frac{\mathrm{v}_1}{\mathrm{v}_2}=\frac{3}{2} \\
& \mathrm{~m}_1 \mathrm{v}_1=\mathrm{m}_2 \mathrm{v}_2 \Rightarrow \frac{\mathrm{m}_1}{\mathrm{~m}_2}=\frac{2}{3}
\end{aligned}
$$
Since, Nuclear mass density is constant
$$
\begin{aligned}
& \frac{\mathrm{m}_1}{\frac{4}{3} \pi \mathrm{r}_1^3}=\frac{\mathrm{m}_2}{\frac{4}{3} \pi \mathrm{r}_2^3} \\
& \left(\frac{\mathrm{r}_1}{\mathrm{r}_2}ight)^3=\frac{\mathrm{m}_1}{\mathrm{~m}_2} \\
& \frac{\mathrm{r}_1}{\mathrm{r}_2}=\left(\frac{2}{3}ight)^{\frac{1}{3}} \\
& 	ext { So, } \mathrm{x}=2
\end{aligned}
$$

Atoms & Nuclei

A nucleus disintegrates into two smaller parts, which have their velocities in the ratio 3 : 2. The ratio of their nuclear sizes will be ${\left( {{x \over 3}} \right)^{{1 \over 3}}}. The value of 'x$' is :-

Integer / Numeric Answer Type