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Unformatted text preview: Physics 212 Problem Set 10 Spring 2010 1. Find all of the allowed spectral terms for the 1 s 2 2 s 2 2 p 3 configuration by proceedings as follows: (a) Why are the spectral terms dictated by only the 2 p 3 part of this configuration? (b) Form the analog of our naive table from class. That is, form a chart of possible L , S , and J values, and identify the resulting terms (of the form (2 S +1) L ) and sublevels (of the form (2 S +1) L J ). In the final column of your table give the degeneracy of each term. Here, ~ L = ~ l 1 + ~ l 2 + ~ l 3 , with an analogous definition for ~ S . ~ J = ~ L + ~ S . This table represents all the possibilities were the particles distinguishable. Some of the entries will be repeated and it is easiest just to include a (x n ) to the left of the table, where n is the number of times that entry appears. Call this Table I. (c) Many of the possibilities appearing in Table I violate the Pauli exclusion principal if the particles are identical. Form a second table, this time in the individual particle basis, which gives all of the possibilities consistent with the Pauli exclusion principal. As in class, you will have an m l value table, and use arrows to indicate m s values. Only now you will have three arrows per row instead of two, because now we are looking at a three-valence electron atom. How many possibilities are there? Now input the M L and M S entries in two further columns, where M L = m l 1 + m l 2 + m l 3 , etc. Call this Table II. (d) Now identify the terms in Table I which are allowed by Table II. It may help to proceed as follows: i. Create a table of M L versus M S values. Call it Tabel III. Within the body of the table should be the number of states in Table II with each M L and M S value. ii. Find the largest possible M L value, call it M * L and the largest possible M S value, call it M * S . For your M * L to exist, it must correspond to a value of L * such that L * = M * L . Associated with this L * must be all of the M L values from- L * up to + L * in unit steps. Similarly, for yourin unit steps....
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