4. Discuss how the spin orbit interaction arises in a hydrogen-like system and show that its Hamiltonian takes the form: Hso = {(r)L.S. Show how this gives rise to an energy correction of the form E = a(n, l) [j(j+1)-l(l+1)-s(s+1)], where the symbols have their usual meaning. Show that the spin orbit splitting in any orbital with >0 is not symmetrical. . If a hydrogen atom state was written as 2D3/2 what does this tell you about it? Write out the states that you expect to occur for principal quantum numbers n =3 and n=4. How many component lines are possible for the n = 4 to n = 3 optical transition in atomic hydrogen? Illustrate your answer with a diagram showing the levels and allowed transitions. State the selection rules that you use.

4. Discuss how the spin orbit interaction arises in a hydrogen-like system and show that its Hamiltonian takes the form: Hso = {(r)L.S. Show how this gives rise to an energy correction of the form E = a(n, l) [j(j+1)-l(l+1)-s(s+1)], where the symbols have their usual meaning. Show that the spin orbit splitting in any orbital with >0 is not symmetrical. . If a hydrogen atom state was written as 2D3/2 what does this tell you about it? Write out the states that you expect to occur for principal quantum numbers n =3 and n=4. How many component lines are possible for the n = 4 to n = 3 optical transition in atomic hydrogen? Illustrate your answer with a diagram showing the levels and allowed transitions. State the selection rules that you use.