Spectra of Other Elements

Systems of Terms.

For simplicity it has been assumed in the foregoing description that each member of a spectrum series consists of a single line. This is sometimes the case, but more often the lines are double, triple, or even more complex. For example, in the spectra of the alkali metals the series consists of a succession of double lines, which in the spectra of the lighter elements are so close together as to appear single under small dispersion. (See Plate II., Nos. 8 and 9.) In zinc and certain other elements there are series of triplets. The complica tions which this multiplicity introduces, though they were origi nally disentangled from observations of the lines themselves, can be best described by considering the terms, for the relations are there seen in their greatest simplicity.

It appears that terms may be classified in systems, known as singlets, doublets, triplets, etc., up to a limit which is theoretically indefinite but in practice rarely exceeds the multiplicity of octets. In a singlet system, all the terms, of whatever type, are single, like those considered in the last section. In a doublet or triplet system, all the terms are double or triple except the S terms, which are single in each case. In a quartet system, all the terms are quadruple except the S terms, which are single, and the P terms, which are triple. These and other apparently irregular complexities are special examples of a general rule, viz.—The multiplicity of a term is as large as possible subject to (a) never exceeding the multiplicity indicated by the name of the system to which it belongs; and (b) never exceeding i for an S term, 3 for a P term, 5 for a D term, 7 for an F term, etc. From this rule the multiplicities of the terms in any system can be at once written down.

Term Notation.

It is necessary now to elaborate the symbol representing a term so that it shall, first, indicate the system to which a term belongs, and secondly, in the case of a com ponent of a multiple term, distinguish it from the other com ponents. The system is indicated by an index at the top left hand corner, and the component number by a suffix on the right. For example, in a quartet system, the P terms are represented by m4P2, m4p3. The particular figures used as suffixes are of no importance so far as the mere identification of terms is con Selection Rules.—The reason for adopting these particular figures is that in combinations between multiple terms, another "selection rule" comes into operation, so that the combinations which are numerically possible do not all occur. Consider, for example, a combination between a P and a D term in a quartet system. The former is triple and the latter quadruple, and if each P component combined with each D component to give a spectrum line there would thus be 12 lines in all. As a matter of fact, however, only 8 appear, and by choosing the suffix numbers according to the above table, these particular lines can be indi cated by a very simple rule, viz.—only those combinations occur for which the suffix numbers differ by zero or unity. Thus, writ

ing the component terms as co-ordinates, and putting a cross at the position of each possible combination, we find the following group of eight lines as a typical quartet PD combination, or mu/tip/et, as it is called :— Such a group of lines, it must be understood, is the analogue of a single line in a singlet system, and a succession of such groups in which the P component terms are the same and the D terms have consecutive values of m, constitutes a diffuse series in a quartet system.

It will be convenient at this stage to summarise and somewhat amplify the foregoing analysis, and at the same time to introduce a nomenclature derived from theoretical considerations which is in common use. A term is completely specified by four quanti ties :—(I ) Its type—S, P, D, etc. This is sometimes represented by its azimuthal quantum number, and indicated by the letter k. For an S term, k= 1; for a P term, k = 2, and so on. (2) Its principal quantum number, n, for which a serial number m is usually substituted in series formulae as above. (3) Its system— generally called the multiplicity, and denoted by the letter r. (4) Its suffix number, or inner quantum number, represented by j. In expressing a term, the azimuthal quantum number is rarely used, the corresponding type symbol, S, P, D, etc., being retained instead : thus, represents the second component of a D term in a triplet system for which the serial number is 4. A perfectly general representation of a term is nrkj.

When two terms combine to give a spectrum line they must satisfy the following conditions simultaneously:—(r) The differ ence of the r values must be o or This means that terms of different multiplicities may combine with one another, but the multiplicities must be both even or both odd. (2) The difference of the k values must be -±1. (3) The difference of the j values must be o or 1. There is one exception to the third rule; namely, that if the j value is o for both terms, the combination does not oc cur. These three conditions do not involve the n values, which take no part in restricting the possible combinations of terms. It should be mentioned that there are also certain definite relations between the intensities of the lines in a particular combination of multiple terms, which are connected with the values of the inner quantum numbers. In theoretical discussions, intensities rank only second to wave-numbers, and much attention has been given to their exact measurement by Ornstein and others. The second and third selection rules are illustrated in fig. 16, which shows the structure of some of the doublet and triplet combina tion groups. The k rule, for example, forbids the combination SD, and the j rule reduces the number of lines in each group as compared with the number which is arithmetically possible, except in the SP group. The strongest lines of a group are those for which j changes in the same direction as k, and the intensity dimin ishes with the values of j which are involved.