For a first-order reaction, the relationship between half-life ($t_{1/2}$) and the rate constant ($k$) is given by the equation:

$t_{1/2} = \frac{0.693}{k}$

Rearranging the formula to solve for the rate constant $k$:

$k = \frac{0.693}{t_{1/2}}$

Given the half-life $t_{1/2} = 1386 \text{ s}$, substituting this value into the equation:

$k = \frac{0.693}{1386} = \frac{693}{1386 \times 1000} = \frac{1}{2000} \text{ s}^{-1}$

$k = 0.0005 \text{ s}^{-1} = 5.0 \times 10^{-4} \text{ s}^{-1} = 0.5 \times 10^{-3} \text{ s}^{-1}$

Therefore, the specific rate constant of the reaction is $0.5 \times 10^{-3} \text{ s}^{-1}$.