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Question

(C) The initial mass of the parent nucleus is $M$. It splits into three daughter nuclei,each of mass $m = M/3$.The energy released in the fission reac

Vedclass · Accepted Answer

$c \sqrt{\frac{2 \Delta M}{M}}$

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(C) The initial mass of the parent nucleus is $M$. It splits into three daughter nuclei,each of mass $m = M/3$.The energy released in the fission reaction is given by Einstein's mass-energy equivalence: $E = \Delta M c^2$.This energy is converted into the kinetic energy of the three daughter nuclei. Let $v$ be the speed of each daughter nucleus.The total kinetic energy is $K.E. = 3 	imes (\frac{1}{2} m v^2) = 3 	imes (\frac{1}{2} 	imes \frac{M}{3} 	imes v^2) = \frac{1}{2} M v^2$.Equating the energy released to the kinetic energy: $\Delta M c^2 = \frac{1}{2} M v^2$.Solving for $v$: $v^2 = \frac{2 \Delta M c^2}{M}$.Therefore,$v = c \sqrt{\frac{2 \Delta M}{M}}$.

In a nuclear fission reaction of an isotope of mass $M$,three similar daughter nuclei of the same mass are formed. The speed of a daughter nucleus in terms of mass defect $\Delta M$ will be:

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