# (a) How many sub-shells are associated with n = 4?

Question:

(a) How many sub-shells are associated with = 4?

(b) How many electrons will be present in the sub-shells having $m_{s}$ value of $-1 / 2$ for $n=4 ?$

Solution:

(a) $n=4$ (Given)

For a given value of ' $n$ ', ' $r$ can have values from zero to $(n-1)$.

$\therefore I=0,1,2,3$

Thus, four sub-shells are associated with n = 4, which are spd and f.

(b) Number of orbitals in the $n^{\text {th }}$ shell $=n^{2}$

For $n=4$

Number of orbitals = 16

If each orbital is taken fully, then it will have 1 electron with $m_{s}$ value of $-\frac{1}{2}$.

$\therefore$ Number of electrons with $m_{s}$ value of $\left(-\frac{1}{2}\right)$ is 16 .