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Walter J. Balfour and Thomas W. Dingle Universitv of Victorla Victoria. B.C. ~anadaV8W 2Y2
Quantum Defects from Atomic Spectra
The study of atomic spectra in the undergraduate physical chemistry laboratory provides a useful introduction to elementary quantum mechanics and the understanding of atomic structure. Typical experiments on the alkali metals have been described in this and standard laboratory texts.4 A common experiment is one in which the student records the atomic emission spectrum of sodium, for example, and measures the wavelengths of all observed lines. Then, given the analysis of the spectrum in terms of the energy levels involved for each line, he can determine the ionization potential LP. and quantum defects, 61, for the various emission series from the energies En! of the atomic levels. Relative to that of the ground state (taken at zero)
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Enl = I.P. - R l ( n 61)' (1) The quantum defect &, which depends on the degree of penetration of the outer electron into the core, has a different value for different values of 1. It is not a trivial mathematical exercise to enter the measured En, values into eqn. (I) and solve for I.P. and 61. Bettelheim4 suggests a method which leads to a cubic equation in (n - 61). As an alternative we have found that the following simple graphical procedure gives reliable results. It has the advantage of treating all data in a given series simultaneously. Moreover, the procedure provides visually a means whereby the student can check whether his data are reasonable since any anomalous points are immediately obvious from the graph. First, one assumes that 61 is zero and plots En[against l l n 2 for the different spectral series. Extrapolation of the resulting curves to lln2 = 0 gives an initial estimate of I.P. which then allows an initial value of 6[ to he determined from where n is the principal quantum numt,er of ihr lowrat 00served energy I t 4 for the s~~ecitied I. One next pl~ltithe experimental E,I against l l ( n - 602. The graphs are now more nearly linear and an improved estimate of I.P. is obtained which, in turn, gives an improved estimate of 61, etc. With sodium data taken on a Baird-Atomic 1.5-m spectograph, where errors in measurement are
