Given that the equilibrium constant for the reaction $2{\text{SO}}_{2(\text{g})}+{\text{O}}_{2(\text{g})}\rightleftharpoons 2{\text{SO}}_{3(\text{g})}$ has a value of $278$ at a particular temperature. What is the value of the equilibrium constant for the following reaction at the same temperature:
$${\text{SO}}_{3(\text{g})}\rightleftharpoons {\text{SO}}_{2(\text{g})}+\frac{1}{2}{\text{O}}_{2(\text{g})}$$

1. A
   $1.3\times 10^{-5}$
2. B
   $1.8\times 10^{-3}$
3. C
   $3.6\times 10^{-3}$
4. D
   $6.0\times 10^{-2}$