A nucleus of uranium decays at rest into nucl | vedclass

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(D) Since the uranium nucleus is at rest,the initial momentum is $0$. By the law of conservation of linear momentum,the total final momentum must also

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the helium nucleus has more kinetic energy than the thorium nucleus

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(D) Since the uranium nucleus is at rest,the initial momentum is $0$. By the law of conservation of linear momentum,the total final momentum must also be $0$.Therefore,the magnitude of the momentum of the thorium nucleus $(P_{Th})$ must be equal to the magnitude of the momentum of the helium nucleus $(P_{He})$,i.e.,$P_{Th} = P_{He} = P$.The kinetic energy $(KE)$ of a particle is given by the formula $KE = \frac{P^2}{2m}$,where $m$ is the mass.Thus,$KE_{Th} = \frac{P^2}{2m_{Th}}$ and $KE_{He} = \frac{P^2}{2m_{He}}$.Since the mass of the helium nucleus $(m_{He})$ is significantly smaller than the mass of the thorium nucleus $(m_{Th})$,the kinetic energy of the helium nucleus $(KE_{He})$ will be greater than the kinetic energy of the thorium nucleus $(KE_{Th})$.Hence,option $(D)$ is correct.

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

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