(Useful constants: R=109677.581cm1;1cm111.958Jmol1.) 5.1 Calculate the first three lines in the absorption spectrum arising from transitions from the 3s level of the hydrogen atom. What is the ionization energy of this level? 5.2 The term symbol for a particular atomic state is quoted as 4D5/2. What are the values of L,S, and J for this state? What is the minimum number of electrons which could give rise to this? Suggest a possible electronic configuration. 5.3 What are the term symbols for the following pairs of non-equivalent electrons: (a)ss,(b)pp,(c)sd, and (d)pd ? ELECTRONIC SPECTROSCOPY OF ATOMS 161 5.4 What are the term symbols for the following pairs of equivalent electrons: (a)s2,(b)p2, and (c)d2 ? 5.5 The term symbols for particular states of three different atoms are quoted as 4S1,2D7/2, and 0P1; explain why these are erroneous. 5.6 Figure 5.7 shows the three transitions arising between 2P and 2D states. Into how many lines would each of these transitions split if a magnetic field were applied? (Assume that the g-value is different for each energy level.) 5.7 The ground state electron configuration of phosphorus is 1s22s22p63s23p3. Ignoring spin-orbit coupling, find the terms for this state and identify that which is lowest in energy. 5.8 Work out the lowest energy terms for the following atoms, including spin-orbit coupling (the essential part of the electron configuration is given in brackets): Ru(4d75s);La(5d6s2);Nb(4d45s);Ca(4s2)Eu(4f76s2);Gd(4f75d6s2);Ag(4d105s);W(5d46s2);Pt(5d96s) 5.9 What are the electron configurations for the ground state and first excited state of the Tl+ion? List the terms which arise from each of these configurations, including spin-orbit coupling. Place the levels in order of increasing energy. The observed energies of the lowest four levels are: (a) zero (by convention); (b) 49451cm1; (c) 52393cm1 (d) 61725cm1. According to the Rssell-Saunders coupling scheme, the energy separation between adjacent spin-orbit coupling levels from a given term should be l times the larger value of J (e.g. 3l between levels with J=2 and J=3 ), where l is the spin-orbit coupling constant. On this basis, what would you expect the relative sizes of the energy gaps (b)(c) and (c)(d) to be, and why