Using Table 22.3, which lists the possible terms that arise...

Using Table $22.3,$ which lists the possible terms that arise from a given configuration, and Hund's rules, write the configurations and term symbols for the ground state of the ions $\mathrm{F}^{-}$ and $\mathrm{Ca}^{2+}$ in the form $^{(2 S+1)} L_{J}$.

Key Concepts

Angular Momentum Coupling

Angular momentum coupling in atoms involves combining the individual electron spin and orbital angular momenta to form total spin (S) and total orbital angular momentum (L). The way these momenta couple determines the quantum states that the electrons can occupy and underlies the derived term symbols. This coupling is critical for understanding the spectral lines and magnetic properties of atoms, as well as applying Hund's rules accurately.

Hund's Rules

Hund's rules are empirical guidelines used to determine the lowest energy (ground state) term among the possible terms that arise from a given electron configuration. They state that the term with the highest multiplicity (largest spin, S) lies lowest in energy, followed by the term with the highest orbital angular momentum (L) for a given multiplicity, and finally, the total angular momentum (J) is considered, with its ordering depending on whether the subshell is more or less than half-filled.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom or ion's atomic orbitals. It provides the basis for determining the chemical and spectroscopic properties of a species by indicating which orbitals are filled and how many electrons they contain. In ions, electrons are added or removed relative to the neutral atom, leading to configurations that often correspond to closed shells or noble gas configurations, which are generally associated with enhanced stability.

Term Symbols

Term symbols are a concise notation used in atomic spectroscopy to represent the quantum state of an atom. They encapsulate the total spin (S), the total orbital angular momentum (L), and the total angular momentum (J) through the notation ^(2S+1)L_J. This notation provides important information about the energy levels, degeneracies, and selection rules for transitions between states.

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