The relation between ${\mathrm{n}}_{\mathrm{m}}$ (${\mathrm{n}}_{\mathrm{m}}=$the number of permissible values of magnetic quantum number $\left(\mathrm{m}\right)$) for a given value of azimuthal quantum number $\left(\mathrm{l}\right)$, is

The possible magnetic quantum number values for a given value of azimuthal quantum number $\mathrm{l}$ are $-\mathrm{l} \mathrm{to} +\mathrm{l}$ through $0$. Suppose if $\mathrm{l}=1$, the possible ${\mathrm{n}}_{\mathrm{m}}$ values are $-1,0,+1$. The mathematical formula can be written as follows,

$$\begin{gathered} {\mathrm{n}}_{\mathrm{m}}=2\mathrm{l}+1 \\ \Rightarrow \mathrm{l}=\frac{{\mathrm{n}}_{\mathrm{m}}-1}{2} \end{gathered}$$