The Rydberg-Schuster Law and the Analysis of Atomic Spectra Recently, Miller' reported on the analysis of the atomic lithium spectrum by usinga match of energy differences for all possible transitions in the spectrum to a table of A,,(6)
= [l/(m - 612] - [l/(n
- 6P]
i o r r h CN. ~ n = ni T I 91111 ~ i t chm i t ; t n ~quantum defect A. Alrho~~gh ir iq then pwiible tuditfercntiatr the apprtrnl hnes 111111 thrtt. -.t-riec(which hme d ~ f f w m tvnlurs uf6, the identity of tlltsc series isonly fwmd lr) reference to rhr results u i a m;~gn* i r l d The h ~ m r i r a l l yImpurlant Kydtwrg-Srhuster Lew- molder the s r r i e ~to he ident~fiedinnn the pnflperties of the series. A series A is characterized by a series limit Ta, a constant quantum defect SA and consecutive integers mi:
(l1An.i = TA - Rl(mi - 6nI2
(1)
As can be seen, (11A)a.jconverges as mi increases, and this fact can simplify carrying out the match of energy differences
with the table A,,(6). The Law says that the sharp and diffuse-series limits (T,. T o ) are equal and that their difference from the principal series limit Tois To - T h = (1IA)m = -(l/h),,o
(2)
(l/A),n is the hv~othetical (extra~olated)zeroth member of the s h a r ~s e r k 3 The first eoualitv .. . . identifies the orinci~al seriesand the second the sharp and diffuse s e r i a 4 From eqn. (2) we deduce, using eqn. (I),that
That is, T,!o is theatomic level which forms the initial state of the transition which is the first member of the principal series; T, is the atomic level which is of the same type as those giving rise t o the sharp series transitions, and it is the lowest level of all (i.e., the ground state level). We now have all the information necessary to draw the energy level diagram and, by using the diagram, can 'explain' the validity of the Rydberg-Sehuster Law. 'Miller. K. J.. J. CHEM. EDUC... 51.805 (1974). . . ~ . W h l t r . 11. ('.. "lntrwlw~i
