MULTIELECTRON ATOMS

The energy levels and optical spectra are much more complicated for atoms with more than one electron in the outer shell. In this section we will discuss qualitatively the energy levels for helium and the alkali earths, atoms in the second column of the periodic table. These atoms all consist of a core of electrons plus two electrons in an outer s shell. Most of the observed spectra can be understood in terms of energy levels corresponding to the raising of one of these electrons to a shell or subshell of higher energy. These are called normal levels. Energy levels involving excitation of both outer electrons are called anomalous and will be discussed only briefly here. The model used to calculate the energy levels for these atoms consists of two identical electrons moving in a potential due to the nucleus and the core electrons. The simplest such atom is helium, but beryllium, magnesium, calcium, strontium, barium, and radium are all very similar. Let us consider magnesium (Z ϭ 12) as a specific example. The ground-state electron configuration is (1s 2 2s 2 2p 6)3s 2. In the ground state both outer electrons have the same space quantum numbers 1n = 3, / = 0, m / = 02, so the resultant spin must be zero. When one of the electrons is excited to a higher energy state such as 3p, the spatial quantum numbers are no longer the same, so the resultant total spin need not be zero. For example, the resultant spin S for two particles with spin s = 1 2 can be either S ϭ 0 (antiparallel spins) or S ϭ 1 (parallel spins). If S ϭ 0, the total angular momentum of the atom is due entirely to the orbital angular momentum of the excited electron, so j = /. The S ϭ 0 states are called singlet states. If S ϭ 1, there are three possible values for the total angular momentum number j corresponding to the three possible orienta-tions of S relative to L: j = / + 1, j = /, or j = /-1 (except if / = 0, in which case j = / is the only possibil