Question

4. Obtain the spectroscopic designation for the following three electronic configurations (a) 1s 2s2(b) 1s'2s2p (d) Obtain the energy levels of the first excited state of a helium atom and designate the different levels using LS coupling scheme. (c) 1s 2s3d

Answer 1

Spectroscopic notation 2a + 1 L_J Whenever we have closed shell its spectroscopic symbol is^1_0S. 1 S^2 2S^2 Since it is a closed shell so term symbol is: S^1_0 1S^2 2S 2p here 1S^2 is closed shell term symbol is S^1_0 2S 2p for S l_1 = 0 for p l_2 = 1 L = Vertical-bar l_1 + l_2 Vertical-bar to Vertical-bar l_1 - l_2 Vertical-bar for S S_1 = 1/2 S = Vertical-bar s_1 + s_2 Vertical-bar to Vertical-bar s_1 - s_2 Vertical-bar for p s_2 = 1/2 S = 1 1 or 0 Thus: for S = 1 J varies as Vertical-bar L + S Vertical-bar to Vertical-bar L - S Vertical-bar L^2s + 1_J: P^3_2, P^3_1, P^3_0 for S = 0: P^1_1 So term symbol: S^1_0, P^1_0, P62_2, 1, 0. 1S^2 2S 3d 2S 3d l_1 = 0 l_2 = 2 = > L = 2 L_2 = 2 s_1 = 2 s_2 = 1/2 = > S = 1, 0 \r\n The first excited state of helium atom correspond to one