Chemistry Question from JEE Main 2026 · 28 January, Shift 2

Consider the following two first-order reactions:

$A \to B$ (first reaction) $C \to D$ (second reaction)

The rate constant for first reaction at $500 \, \text{K}$ is double of the same at $300 \, \text{K}$. At $500 \, \text{K}$, $50\%$ of the reaction becomes complete in $2 \, \text{hours}$. The activation energy of the second reaction is half of that of first reaction. If the rate constant at $500 \, \text{K}$ of the second reaction becomes double of the rate constant of first reaction at the same temperature; then rate constant for the second reaction at $300 \, \text{K}$ is _____ $\times 10^{-1}\,hour^{-1}$ (nearest integer).