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Question:

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

The helium nucleus has less kinetic energy than the thorium nucleus.

The helium nucleus has more kinetic energy than the thorium nucleus.

The helium nucleus has less momentum than the thorium nucleus.

The helium nucleus has more momentum than the thorium nucleus.

Solution:

Since there is no external force acting on the uranium nucleus, momentum will be conserved in the reaction. Piu=0
Final momentum of the Thorium and He nuclei will be zero.
pTh=pHe
KETh=pTh2/2mTh
KEHe=pHe2/2mHe
→KETh/KEHe=pTh2/2mTh / pHe2/2mHe
→KETh/KEHe=mHe/mTh
Since mHe<mTh, KEHe>KETh