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 nccleus

Answer

C

Explanation

If `P _(Th) and P_(He)` are the momenta of thorium and helium bnuclei respectively, then according to law of conservation of linear momentum
`0= P _(Th) + P _(He) or P _(Th) =- P _(He)`
- ve sign shown that both are moving in opposite direactions. But in magnitude
`P _(Th) = P_(He) If ""^(m) TH and ""^(m)He` are the masses of thorium and helium nuclei respectively, then Kinetic energy of thorium nucleus is
`K_(Th) = (p _(Th) ^(2))/(2m _(Th))`
`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`
Thus the helium nucleus has more kinetic energy than the thorium nucleus.