The relation between $n_m$ ($n_m$ = number of permissible values of magnetic quantum number, $m_l$) for a give

Question

The relation between $n_m$ ($n_m$ = number of permissible values of magnetic quantum number, $m_l$) for a given value of azimuthal quantum number ($l$) is:

Accepted Answer

According to the NCERT text, for a given value of the azimuthal quantum number ($l$), the magnetic orbital quantum number ($m_l$) can have $(2l + 1)$ values (ranging from $-l$ to $+l$).

Let $n_m$ be the number of permissible values of $m_l$.
$$n_m = 2l + 1$$

To find the relation for $l$, we rearrange the equation:
$$n_m - 1 = 2l$$
$$l = \frac{n_m - 1}{2}$$

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