1. a) An electron has orbital angular momentum l = 2 and spin angular momentum s

Question

1. a) An electron has orbital angular momentum l = 2 and spin angular momentum s = 1/2. What are the allowed values of its total angular momentum j ?

b) i) The 2p3p conguration has terms 1S, 3S, 1P, 3P, 1D, 3D but the 2p2 conguration only has terms 1S, 3P, 1D. Why?

ii) Which terms of the 2p2 conguration interact with the 2s2 1S?

iii) Identify the operator which gives rise to this interaction.

c)i) Why is the following electric dipole radiative transition forbidden in LS coupling? 1s2p3P 1s2 1S+ . [1] ii) Which J-value of the 3PJ gives rise to an allowed electric dipole radiative transition in intermediate coupling?

iii) Why is the transition now allowed?

Explanation / Answer

Given that l = 2

spin s = 1/2

The total angular momentum has values from l-s to l+s with the difference of 1.

Now j has values 2-1/2 to 2+1/2 i.e. 3/2 to 5/2.

The possible values are 3/2 or 5/2.

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