Nitrogen dioxide $(N{O}_2)$ is a serious air pollutant. The question arises: To what extent does $N{O}_2$ tend to form from $N_2$ and $O_2,$ which are normal components of the air? To find an answer, scientists study the following reactions involving oxides of nitrogen and establish their equilibrium constants $($all measurements at $25C)$:

$NO(g)+\frac{1}{2}{O}_2(g)N{O}_2(g)$

$\frac{1}{2}{K}_2(g)+\frac{1}{2}{O}_2(g)1\mathrm{.}3{10}^6$

$K_2=6\mathrm{.}5{10}^{-16}$

Find the equilibrium constant $K_3$ for the following $N{O}_2$ forming reaction at $25C$ :

$N_2(g)+2O_2(g)2N{O}_2(g),K_3=?$