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Question: spinorbit interaction question the answer to the first bit is...

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Spin-orbit interaction question. The answer to the first bit is j=7/2, 9/2 with energy splitting (9/2)*A*(h-bar)^2. The splitting in the second part is 5.2*10^-5 eV. Please can you explain how to get these answers? Particularly why j takes those values, that’s the part I really don’t get.
The outer electron of a neutral potassium atom is in a 3g orbital. Show that there are two possible values for its energy, and find the difference between these values in terms of the constant A Describe what happens to these two 3g levels when the atom is placed in a weak magnetic field B. Calculate the splitting between the states of the lower level for a field of strength B-1T.
In this second case the j values are 3/2 and 5/2, why is this case different?
The low-energy states of Ti3+ ions have L-2 and S = 1/2. The spin-orbit interac- tion Hamiltonian for the ions can be taken to have the form H80 = ALS, where A is a constant. List the possible values of J and determine the resulting energy shifts for each of these states.
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