Question

Explain
(a) The pauli exclusion principle, and
(b) Hund's rule.
Show how these are used to specify the electronic arrangements of the first 20 elements in the periodic table.

Answer 1

Hint: The Pauli’s exclusion principle relates to the filling up of electrons in the shell, and the Hund’s rule relates to pairing up of electrons in degenerate orbitals.

Complete answer:
Pauli’s Exclusion Principle: This principle was given by Wolfgang Pauli (1926). This principle actually excludes the possibility of any two electrons having all the same four quantum numbers i.e., 'No two electrons in an atom can have the same set of four quantum numbers'. Because the n, I and m, quantum numbers address a particular orbital. The four quantum numbers required to define the spin of the electron orbital. It can have only two possible values i.e.,$+{\displaystyle \frac{1}{2}}$ and $-{\displaystyle \frac{1}{2}}$. Therefore a maximum of only two electrons can be accommodated in an atomic orbital and these two electrons must have opposite spin.
For example, helium has two electrons $1s^2$ that have the same n, l, m values but different values of spin.
Hund’s Rule: The rule deals with the filling of electrons in the equal energy (degenerate) orbitals of the same subshell. This rule says that ``no pairing of electrons starts in any of the degenerate orbitals until all the orbitals of the subshell contain one electron each with parallel spin". Example : Each of the three p-orbitals of the p-subshell gets one electron of parallel spin before any one of them receives second electrons of opposite spin.

Note: The Pauli’s Exclusion principle, in a nutshell can be said as: “ The maximum number of electrons that can be accommodated in a particular shell is $2n^2$.