$$\begin{gathered} \mathrm{For} \mathrm{first} \mathrm{order} \mathrm{reaction}, \\ \mathrm{A}\to \mathrm{B} \\ \text{Rate}=\mathrm{k}\times \left[\mathrm{A}\right] \\ \text{Given, rate}=2.0\times {10}^{-5}{\mathrm{molL}}^{-1}{\mathrm{s}}^{-1} \\ \left[\mathrm{A}\right]=\text{ Conc. of }\mathrm{A}=0.01\mathrm{M} \\ \text{ So, }2.0\times {10}^{-5}=\mathrm{k}\times 0.01 \\ \begin{array}{rl} & \mathrm{k}=\frac{2.0\times {10}^{-5}}{0.01}{\mathrm{s}}^{-1}\\ & =2.0\times {10}^{-3}{\mathrm{s}}^{-1}\end{array} \\ \text{ For first order reaction, } \\ \begin{array}{rl} & {\mathrm{t}}_{1/2}=\frac{0.693}{\mathrm{k}}=\frac{0.693}{2.0\times {10}^{-3}}\\ & =346.5=347\mathrm{s}\end{array} \end{gathered}$$