A nucleus of uranium decays at rest into nuclei of thorium and helium. Then :

Options

A. The helium nucleus has more momentum than the thorium nucleus.
B. The helium nucleus has less kinetic energy than the thorium nucleus.
C. The helium nucleus has more kinetic energy than the thorium nucleus.
D. The helium nucleus has less momentum than the thorium nucleus.

Explanation

If `vecp_("Th")+vecp_("He") or vecp_("Th")=-vecp_("He")`
`-ve` sign shows that both are moving in opposite directions.
But in magntitude
`p_("Th")=p_("He")`
If `m_("Th") and m_("He")` are the masses of rhorium and helium nuclei respectively, then
Kinetic energy of thorium and helium nuclei respectively, then
Kinetic energy of thorium nucleus is `K_("Th")=(p_("Th")^(2))/(2m_("Th"))`
and that of helium is
`K_(He)=(p_(He)^(2))/(2m_(He))`
`therefore" "(K_(Th))/(K_(He))=((p_(Th))/(p_(He)))^(2)((m_(He))/(m_(Th)))`
But `p_("Th")=p_("He") and m_("He") lt m_("Th")`
`therefore" "K_("Th") lt K_("He") or K_("He") gt K_("Th")`
Thus the helium nucleus has more kinetic energy than the thorium nucleus.