Question 290: Atoms & Nuclei

Question

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

Accepted Answer

From conservation of momentum $${m_1}{v_1} = {m_2}{v_2}$$
$$ \Rightarrow \left( {{{{m_1}} \over {{m_2}}}} \right) = \left( {{{{v_2}} \over {{v_1}}}} \right)\,\,$$ given $$\,\,{{{v_1}} \over {v{}_2}} = 2$$
$$ \Rightarrow {{{m_1}} \over {{m_2}}} = {1 \over 2}$$
$$ \Rightarrow {{r_1^3} \over {r_2^3}} = {1 \over 2}$$
$$ \Rightarrow \left( {{{{r_1}} \over {{r_2}}}} \right) = {\left( {{1 \over 2}} \right)^{1/3}}$$

Answer

$${3^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}:1$$

Answer

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

Answer

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

Answer

$$1:{3^{{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}}$$

Atoms & Nuclei

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

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