For the reaction \[{{N}_{2}}(g)+{{O}_{2}}(g)2\] \[NO(g),\] the equilibrium constant is \[{{K}_{1}}\]. The equilibrium constant is \[{{K}_{2}}\] for the reaction \[2NO(g)+{{O}_{2}}(g)2N{{O}_{2}}(g)\] What is K for the reaction \[N{{O}_{2}}(g)\frac{1}{2}{{N}_{2}}(g)+{{O}_{2}}(g)\]? [AIPMT (S) 2011]