Question

Explain Hund's rule and spectroscopic term of the ground state of an atom?

Answer 1

Hund's rule

• Before any orbital is doubly occupied, all orbitals in the sub-level are singly occupied.
• All electrons in a single-occupancy orbital have the same spin in order to maximize overall spin.
• An electron can fill all of its orbitals with the same energy.
• Therefore it will not be coupled with another electron in an orbital that is only partially filled.
• Atoms in their ground state have a lot of unpaired electrons.
• The behavior of two electrons in contact would be similar to that of two magnets.
• Before having to pair up, the electrons first attempt to separate themselves from one another as much as they can.
• Example: Carbon with atomic number $6$, hence its electronic configuration is $1s^{2}2s^{2}2p^2$.

Spectroscopic term of the ground state of an atom

• The term symbol in quantum mechanics is an abbreviation for the entire quantum numbers of angular momentum in an atom with multiple electrons.
• However, a term symbol can also be used to denote the quantum mechanical states of a single electron.
• The ground state given is as follows:

${}^{2\mathrm{S}+1}\mathrm{L}_{\mathrm{J}}$

• $2\mathrm{S}+1$ is the maximum multiplicity.
• $\mathrm{L}$ is the total orbital angular momentum.
• $\mathrm{J}$ is the total angular momentum.
• $\mathrm{J}$ is equal to $\mathrm{L}+\mathrm{S}$ for more than half-filled degenerate orbitals.
• $\mathrm{J}$ is equal to will be equal to $\mathrm{L}-\mathrm{S}$ for equal and less than half- filled degenerate orbitals.
• For example, Carbon atom term symbols are ${}^1\mathrm{S}_0,{}^3\mathrm{P}_0,{}^3\mathrm{P}_1,{}^3\mathrm{P}_2$ and ${}^3\mathrm{D}_2$