Question

What are term symbols? What should I know about ground-state atomic term symbols?

Answer 1

Hint: The Rydberg–Ritz combination principle, an actual finding that the wavenumbers of spectral lines may be represented as the difference of two terms, underpins the use of the word term for an energy level. This was eventually summarised by the Bohr model, which associated quantized energy levels with terms and photon energies with spectral wavenumbers .

Complete answer:
The word symbol is an abbreviated description of the (total) angular momentum quantum numbers in a multi-electron atom in quantum mechanics (however, even a single electron can be described by a term symbol). Because the energy level also depends on the total angular momentum including spin, each energy level of an atom with a particular electron configuration is defined by not only the electron configuration but also its own term symbol. LS coupling (also known as Russell–Saunders coupling or spin-orbit coupling) is assumed by the standard atomic term symbols. Hund's rules anticipate the ground state term symbol.
The spin–orbit interaction (or coupling) is weak in light atoms, resulting in excellent quantum numbers for total orbital angular momentum L and total spin S. LS coupling, also known as Russell–Saunders coupling or spin-orbit coupling, is the interaction between L and S. The term symbols of the type are then used to denote atomic states.
${}^{2S+1}{L}_J$
Ground-state atomic term symbols
Using Hund's principles, calculating the term symbol for an atom's ground state is quite simple. It relates to a state with the highest S and L values.
Begin with the electron configuration that is the most stable. Full shells and subshells are eliminated since they do not contribute to the total angular momentum.
The term symbol is $${}^1{S}_0$$ if all shells and subshells are full.
Apply the Pauli exclusion principle to distribute the electrons among the accessible orbitals. To begin, fill the orbitals with the greatest $m_l$ value with one electron each and assign them a maximum $m_s$ (i.e. $+\frac{1}{2}$). After all orbitals in a subshell have one electron, add a second one (in the same sequence), and give them $m_s$ = $-\frac{1}{2}$.
By combining the $m_s$ values for each electron, the total S is determined. The ground state, according to Hund's first rule, has all unpaired electron spins parallel with the same value of $m_s$ , which is usually selected as $+\frac{1}{2}$. The total S therefore equals $+\frac{1}{2}$ times the amount of unpaired electrons. The total L is computed by summing the $m_l$ values for each electron (thus if two electrons are in the same orbital, multiply the ml by two).
Calculate J as follows: if the subshell is less than half-filled, use the minimum value $$J=|L-S|$$ ; if the subshell is more than half-filled, use the maximum value $$J=L+S$$; if the subshell is half-filled, use the maximum value $$J=S$$

Note:
The National Institute of Standards and Technology has prepared tables of atomic energy levels designated by their word symbols. In this database, neutral atoms are labelled I, singly ionised atoms are labelled II, and so on. In the s-block and p-block elements, neutral atoms have the same term symbol for each column, but the d-block and f-block elements may differ if the ground-state electron configuration varies within a column.