For a first order reaction $\mathrm{A} \rightarrow \mathrm{P}$, the temperature (T) dependent rate constant $(k)$ was found to follow the equation $\log k=-(2000) \frac{1}{\mathrm{~T}}+6.0$. The pre-exponential factor A and the activation energy $\mathrm{E}_{\mathrm{a}}$, respectively, are
Select the correct option:
A
$1.0 \times 10^6 \mathrm{~s}^{-1}$ and $9.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$
B
$6.0 \mathrm{~s}^{-1}$ and $16.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$
C
$1.0 \times 10^6 \mathrm{~s}^{-1}$ and $16.6 \mathrm{~kJ} \mathrm{~mol}^{-1}$
D
$1.0 \times 10^6 \mathrm{~s}^{-1}$ and $38.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$
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