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Question
In a typical fission reaction, the nucleus is split into two middle-weight nuclei of unequal masses. Which of the two (heavier or lighter) has greater kinetic energy? Which one has greater liner momentum?
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Solution
Kinetic Energy (K.E.):
-
The total kinetic energy released is the same for both nuclei together (from conservation of energy).
-
But the lighter nucleus moves faster because the same amount of force acts on both, and lighter mass means higher acceleration.
- Since K.E. = `1/2` mv2, for the same momentum, the lighter particle has higher velocity and hence greater kinetic energy.
- Therefore, the lighter fragment has greater kinetic energy.
Linear Momentum:
- According to law of conservation of momentum, the total momentum before and after fission must be equal (initial momentum = 0).
-
Thus, the two nuclei recoil with equal and opposite momenta.
-
Therefore, both nuclei have equal magnitudes of linear momentum.
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