By now, it should be understood that a system will only absorb (or emit) light if the energy of the light equals the energy difference between the two states involved in a spectroscopic transition. But, there is no guarantee that the transition will occur if this circumstance is met. That is, the Bohr Frequency Condition is a necessary but not sufficient condition for a transition to occur.
Additional criteria for whether an absorption or emission occurs are called selection rules. Selection rules can be grouped into two types, either quantum-mechanical or descriptive (sometimes called "gross selection rules"). That is, some selection rules can be explained using quantum mechanics and wavefunctions and operators and quantum numbers. Other selection rules can be explained by describing what the atom or molecule is doing.
If a transition is favored by a selection rule, we say that the transition is allowed. If a transition does not follow a selection rule, we say that the transition is forbidden. However, since most selection rules are formulated with the assumption of ideality and real systems are not ideal, some forbidden transitions may actually occur. This can understandably confuse the interpretation of a spectrum!
In this chapter, we will look at where these selection rules come from (with the short answer being, of course, quantum mechanics!). First we will consider the more formal mathematical perspective, then we will review a simpler approach based on changes in quantum numbers.
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