Question

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

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

Answer 1

Answer: (D)

Since there is no external force acting on the uranium nucleus, momentum will be conserved in the reaction.
$P _{\text {iu }}=0$
Final momentum of the Thorium and He nuclei will be zero.
$pTh = pHe$
$ KE _{ Th }=\frac{ p _{ Th }^{2}}{2 m _{ Th }} $
$ KE _{ He }=\frac{ p _{ He }^{2}}{2 m _{ He }} $
$\Rightarrow \frac{ KE _{ Th }}{ KE _{ He }}=\frac{\frac{ p _{ Th }^{2}}{2 m _{ Th }}}{\frac{ p _{ He }^{2}}{2 m _{ He }}} $
$\Rightarrow \frac{ KE _{ Th }}{ KE _{ He }}=\frac{ m _{ He }}{ m _{ Th }}$
Since $m_{H e} < m_{T h}, K E_{H e} > K E_{T h}$