Q 12-13-106JEE MainJEE Main 2021 (22 Jul, Shift 1)Easy
A nucleus with mass number 184 initially at rest emits an $\alpha$-particle. If the $Q$ value of the reaction is 5.5 MeV, calculate the kinetic energy of the $\alpha$-particle.
Answer: (D) 5.38 MeV
Momentum is shared equally and opposite between the $\alpha$ (mass 4) and the daughter (mass 180), so kinetic energy divides inversely as the masses:
$$K_\alpha = Q\frac{A - 4}{A} = 5.5\times\frac{180}{184} \approx 5.38\ \text{MeV}$$
Solution by Sreeraj P, M.Sc Physics