Explain the Pauli exclusion principle with an example.

(N/A) The number of electrons that can be filled in various orbitals is restricted by the exclusion principle,proposed by the Austrian scientist Wolfgang Pauli $(1926)$.
Rule: "No two electrons in an atom can have the same set of four quantum numbers $(n, l, m_l, m_s)$."
Alternative statement: Only two electrons may exist in the same orbital,and these electrons must have opposite spins.
According to the rule,two electrons can have the same values for the three quantum numbers $n, l,$ and $m_l$,but they must have different spin quantum numbers ($m_s = +\frac{1}{2}$ and $m_s = -\frac{1}{2}$).
Application: Pauli's exclusion principle helps in calculating the maximum electron capacity of any subshell.
- Subshell $1s$ comprises one orbital; thus,the maximum number of electrons in the $1s$ subshell is two.
- In $p, d,$ and $f$ subshells,the maximum number of electrons is $6, 10,$ and $14$ respectively.

Subshell	Number of orbitals	Maximum electrons $(2 \times \text{orbitals})$
$s$	$1$	$2$
$p$	$3$	$6$
$d$	$5$	$10$
$f$	$7$	$14$

For a principal quantum number $n$,the number of orbitals is $n^2$,and the maximum number of electrons is $2n^2$.
Example: The electron configuration of Helium $(He)$ is $1s^2$. For these two electrons,the values of $n, l,$ and $m_l$ are $1, 0, 0$ respectively. Their spin quantum numbers are $+\frac{1}{2}$ and $-\frac{1}{2}$,which differ from each other.