Q 12-13-028JEE MainJEE Main 2026 (8 Apr, Shift 2)Medium
Two radioactive substances A and B of mass numbers $200$ and $212$ respectively, shows spontaneous $\alpha$-decay with same $Q$ value of $1$ MeV. The ratio of energies of $\alpha$-rays produced by A and B is ______.
Answer: (C) $\dfrac{2597}{2600}$
The parent is at rest, so the alpha and the daughter get equal and opposite momenta. Kinetic energy divides in the inverse ratio of masses:
$$K_\alpha = Q\frac{A - 4}{A}$$
A: $K = \dfrac{196}{200}Q$. B: $K = \dfrac{208}{212}Q$.
$$\frac{K_A}{K_B} = \frac{196 \times 212}{200 \times 208} = \frac{41552}{41600} = \frac{2597}{2600}$$
Solution by Sreeraj P, M.Sc Physics