Chemical Kinetics: JEE Main 2026 Chemistry question

$\mathrm{A \longrightarrow B}$ (first reaction) $\mathrm{C \longrightarrow D}$ (second reaction). Consider the above two first-order reactions. The rate constant for first reaction at 500 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hour. The activation energy of the second reaction is half of that of first reaction. If the rate constant at 500 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 K is ________ $\times 10^{-1}\ \mathrm{hour^{-1}}$ (nearest integer).