In a unimolecular reaction, the rate constants for activation \(\ k_1\) and deactivation \(\ k_{-1} \) of the molecule are \(\ k_1 = 1 \times 10^7 \, \text{s}^{-1} \) and \(\ k_{-1} = 2 \times 10^6 \, \text{s}^{-1} \,\) respectively. The rate constant for the decomposition of the activated molecule \(\ k_2 \ is \ 5 \times 10^5 \, \text{s}^{-1} \). Calculate the effective rate constant \(\ k_{\text{eff}} \) for the overall reaction if the concentration of the reactant molecule is \(\ [A] = 0.1 \, \text{M}.\)
1
\(2 \times10^{6}\ s^{-1}\)
2
\(2 \times10^{5}\ s^{-1}\)
3
\(2.5 \times10^{5}\ s^{-1}\)
4
\(2 \times10^{7}\ s^{-1}\)