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 K is double of the same at 300 K. At 500 K, 50% of the reaction becomes complete in 2 hours. 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 ______ \(\times 10^{-3}\,\text{hour}^{-1}\) (nearest integer).