Microstates degenerate

A multielectron atom can exist in several electronic states, called microstates, which are characterized by the way the electrons are distributed among the atomic orbitals. The number of microstates for a free atom with a valence shell consisting of a set of degenerate orbitals with orbital angular momentum quantum number I housing n electrons is given by ... 

In general, the number of Pauli-allowed microstates (M.S.) can be calculated using the formula given by Equation (4.21), where n is the number of degenerate orbitals and n is the number of electrons to be placed in those orbitals. 

After removal of the five degenerate microstates that comprise the singlet-D term, the microstate table is reduced as follows (Figure 4.18(b)). 

The extraction process is repeated until all of the microstates have been assigned to term symbols. The next extraction removes a term with L= I and S = I, or a triplet-P term. The degeneracy of the state is (2L + I )(2S + I) = 9. Thus, nine microstates must be removed from the table in a symmetrical manner. The table now reduces to Figure 4.18(c). The final term has L = 0 and S = 0, or S, and is singly degenerate. 

When considering the polyelectronic picture, states (or terms) must be used to describe the actual arrangements of the electrons in the valence orbitals. Each term will have a different energy, although it may be composed of a degenerate set of microstates. The terms for the free ion can be determined using methods developed in Chapter 4. 

So it is often useful to switch your attention from microstates to macrostates. For example, for the four-bead polymer, each configuration shown in Figure 10.1 is one microstate. But a typical experiment might only tell you whether the chain is open (four microstates) or compact (one microstate). Then the terms open and compact define macrostates. The density of states W (E) is the number of microstates in a given macrostate. When W > 1, an energy level is called degenerate. 

For a physical system it is always convenient to group microstates with respect to their energies as the energy is a natural quantity that represents the state of a system. However, it is necessary to assume that energetic states can be and are typically degenerate, i.e., different microstates i and j can possess the same energy Ei = Ej. However, the degeneracy... 

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