Q 12-13-056JEE MainJEE Main 2024 (30 Jan, Shift 2)Medium
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 the mass defect $\Delta M$ will be:
Answer: (C) $c\sqrt{\dfrac{2\Delta M}{M}}$
The energy released $\Delta Mc^2$ appears as kinetic energy of three nuclei, each of mass $\approx M/3$ and moving with the same speed $v$:
$$\Delta Mc^2 = 3\times\frac12\cdot\frac M3v^2 = \frac{Mv^2}{2} \Rightarrow v = c\sqrt{\frac{2\Delta M}{M}}$$
Solution by Sreeraj P, M.Sc Physics