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quiz9soln - 1 Problem 1 For the atomic term 3 P what are...

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1 Problem 1 For the atomic term 3 P , what are the energy differences between the levels arising due to spin-orbit coupling. 1.1 Solution For the atomic term 3 P , show the energy differences between the levels arising due to spin-orbit coupling. Answer For this term, the values of J that arise are 0,1,2 and these correspond to L = 1 , S = 1. Thus, E 0 , 1 , 1 = hA 2 [0 - 2 - 2] = - 4 hA 2 E 1 , 1 , 1 = hA 2 [2 - 2 - 2] = - 2 hA 2 E 2 , 1 , 1 = hA 2 [6 - 2 - 2] = 2 hA 2 (1) The energies between levels can be determined by simple subtraction of the values between the J = 0 andJ = 1 states and the J = 1 andJ = 2 states. The results are hA and 2 hA . 2 Problem 2 For the oxygen atom in the ground state, what terms are possible? What is the degeneracy of each term? If spin-orbit coupling is taken into account, what levels arise? What is the degeneracy of each level? 2.1 Solution For the oxygen atom in the ground state, what terms are possible? What is the degeneracy of each term? If spin-orbit coupling is taken into account,
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