Question

A uranium nucleus at rest decays into a thorium nucleus and a helium nucleus, as shown below. Which of the following is true? ${}_{92}^{235}U{\to }_{90}^{231}Th{+}_2^{4}He$.

• A. Each decay product has the same kinetic energy
• B. The decay products tend to go in the same direction
• C. The thorium nucleus has more momentum than the helium nucleus
• D. The helium nucleus has more kinetic energy than the thorium nucleus

Answer 1

The correct option is D The helium nucleus has more kinetic energy than the thorium nucleus

From the law of conservation of momentum, we say that the final momentum of the system must be zero as the initiallly the momentum was zero.

Thus thorium and helium nuclei must move in opposite directions with same magnitude of momentum.

Kinetic energy of nucleus $K=\frac{p^2}{2m}$

where $m$ and $p$ is the mass and momentum of nucleus, respectively.

As we know that mass of helium is less than that of thorium. Hence helium nucleus has more kinetic energy than the thorium nucleus.