520 Quantum Mechanical Basis of Molecular Spectra /27 : 4 



exclusion principle states that the number of quantum numbers which may not 

 be identical is 4. Using this exclusion principle, it is possible to predict the 

 general form of the periodic table. By and large, the lowest values of n and / 

 correspond to the lowest energy levels and these are filled in first. Thus, n — \, 

 1 = 0, rrij = 1/2 corresponds to the lowest level for hydrogen. In helium, both 

 electrons are in the state n = 1, / = but one has m, = +1/2, and the other 

 ntj = — 1/2. The full development is beyond the scope of this text. See, for 

 example, the reference by White.) 



The major energy-level changes are determined by the initial and 

 final values of n and /. Most spectroscopic lines due to electron transi- 

 tions within an atom have a fine structure determined by the quantum 

 number j. Still higher resolution shows that, in many cases, each of 

 these lines has a hyperfine structure. Some hyperfine structure is due 

 to the presence of several isotopes, others to the existence of a net nuclear 

 spin. The nuclear spin has a quantum number /. which is coupled to 

 the total electronic angular momentum specified by J to give a total 

 atomic angular momentum specified by the quantum number K. 



Atomic spectra are employed quite widely in biological research. 

 Perhaps the most frequently used are in flame spectrophotometric studies 

 to identify the amount of sodium, potassium, and calcium in blood, 

 urine, tissues, and food. Atomic spectra due to X-ray absorption are 

 used to locate Ca and other elements within tissues and even within 

 parts of the cells. However, the details of fine and hyperfine structure 

 of atomic spectra are rarely used in biological studies. 



B. Electronic Spectra of Molecules 



The energy states of electrons within a molecule are described by the 

 same types of quantum numbers as those which apply to electrons 

 within an atom. To distinguish the molecular levels from atomic ones, 

 Greek letters are often used. Lower case Greek letters are used to 

 describe the levels of individual electrons within a molecule and capital 

 Greek letters to designate the sums of the electronic properties for the 

 whole molecule. Thus, the total electron spin is represented by the 

 quantum number 2 and the total orbital momentum by the quantum 

 number A. As in atomic spectra, electronic states with a given value of 

 A are designated by the corresponding Greek capital letters ; that is 



A 1 2 3 4 and so on 

 letter 2 n A <D T 



Note that no attention is paid to the order of either the Greek or the 

 English alphabets; rather, the Greek letter closest to the corresponding 

 English letter is used. 



In some cases, the sum of A and 2 is also quantized, just as in atomic 



