Formula to find the types of hybrid orbitals involved in hybridization is:
\(H=\frac{1}{2}[V+M-C+A]\)
Where \(H=\) the number of orbitals involved in hybridization
\(V=\) the number of valence electrons of a central atom
\(M=\) the number of monovalent atoms attached to a central atom
\(C=\) charge on the cation
\(A=\) charge on the anion
\(\mathrm{NO}_{2}{ }^{+}\).
\(V=5, M=0, C=1, A=0 \)
\(\therefore H=\frac{1}{2}[V+M-C+A] \)
\(\Rightarrow H=\frac{1}{2}[5+0-1+0] \)
\(\Rightarrow H=2\)
So, the number of hybrid orbitals is equal to two means the hybridization is sp.
\(\mathrm{NO}_{3}^{-}\):
\(V=5, M=0, C=0, A=1 \)
\(\therefore H=\frac{1}{2}[V+M-C+A] \)
\(\Rightarrow H=\frac{1}{2}[5+0-0+1]\)
\(\Rightarrow H=3\)
So, the number of hybrid orbitals is equal to three means the hybridization is \(\mathrm{sp}^{2}\).
\(\mathrm{NH}_{4}^{+}\):
\(V=5, M=4, C=1, A=0 \)
\(\therefore H=\frac{1}{2}[V+M-C+A] \)
\(\Rightarrow H=\frac{1}{2}[5+4-1+0]\)
\(\Rightarrow H=4\)
So, the number of hybrid orbitals is equal to four means the hybridization is \(\mathrm{sp}^{3}\).
Therefore, the types of hybrid orbitals of nitrogen in \(\mathrm{NO}_{2}{ }^{+}, \mathrm{NO}_{3}{ }^{-}\)and \(\mathrm{NH}_{4}{ }^{+}\)respectively are \(\mathrm{sp}, \mathrm{sp}^{2}\) and \(\mathrm{sp}^{3}\).