Step 1: Write the balanced chemical equation.
Formation of ammonia from constituent elements is:
\[
N_2(g)+3H_2(g)\rightleftharpoons 2NH_3(g)
\]
Step 2: Write the equilibrium constant expression.
For a reaction,
\[
aA+bB\rightleftharpoons cC+dD
\]
the equilibrium constant is
\[
K_c=\frac{[C]^c[D]^d}{[A]^a[B]^b}
\]
Step 3: Apply the formula to ammonia formation.
Thus,
\[
K_c=\frac{[NH_3]^2}{[N_2][H_2]^3}
\]
Step 4: Final conclusion.
Hence, the correct expression is
\[
\boxed{
K_c=\frac{[NH_3]^2}{[N_2][H_2]^3}
}
\]