Question #79044

Consider the following Assertion (A) and Reason (R).\ \textbf{Assertion (A):} A stationary particle of rest mass $M$ undergoes spontaneous decay into two particles of rest masses $m_1$ and $m_2$. If the Q-value of the decay, $Q = (M - m_1 - m_2)c^2$, is comparable to the rest mass energies of the products, the kinetic energy $K_1$ of the particle $m_1$ is INCORRECTLY given by the classical relation $K_1 = Q \left( \frac{m_2}{m_1 + m_2} \right)$.\ \textbf{Reason (R):} The Q-value is a scalar representing the total kinetic energy released, but its distribution is constrained by the vector conservation of linear momentum ($\vec{p}_1 + \vec{p}_2 = 0$). In the relativistic regime, the non-linear relation $E^2 = (pc)^2 + (mc^2)^2$ dictates that the exact kinetic energy is $K_1 = \frac{Q(Q + 2m_2 c^2)}{2Mc^2}$.