For a first order reaction ${\mathrm{t}}_{1/2}$ is $1200 \mathrm{s}.$ The specific rate constant in ${\mathrm{s}}^{-1}$ is

If the rate constants of a reaction at $500 \mathrm{K}$ and $700 \mathrm{K}$ are $0.002 {\mathrm{s}}^{-1}$ and $0.06 {\mathrm{s}}^{-1}$, respectively, the value of activation energy is

$\left(\mathrm{R}=8.314 \mathrm{J} {\mathrm{mol}}^{-1} {\mathrm{K}}^{-1}, \log 3=0.477\right)$