Question 295: Atoms & Nuclei

Question

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

Accepted Answer

The two nuclei have velocity in ratio 8 : 27. By conservation of momentum, we have
$${m_1}{v_1} = {m_2}{v_2} \Rightarrow {{{v_1}} \over {{v_2}}} = {{{m_2}} \over {{m_1}}} \Rightarrow {{{m_2}} \over {{m_1}}} = {8 \over {27}}$$
Now, since $$m = \rho {4 \over 3}\pi {r^3}$$
Therefore, $${{{m_2}} \over {{m_1}}} = {{\rho {4 \over 3}\pi r_2^3} \over {\rho {4 \over 3}\pi r_1^3}} \Rightarrow {{{m_2}} \over {{m_1}}} = {\left( {{{{r_2}} \over {{r_1}}}} \right)^3} \Rightarrow {\left( {{{{r_2}} \over {{r_1}}}} \right)^3} = {8 \over {27}}$$
$$ \Rightarrow {{{r_2}} \over {{r_1}}} = {2 \over 3}$$
Thus, ratio of radii of nuclei $${r_1}:{r_2} = 3:2$$.

Answer

8 : 27

Answer

4 : 9

Answer

3 : 2

Answer

2 : 3

Atoms & Nuclei

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

Choose the correct answer: