- The Hamiltonian Associated With The Spin Orbit Interaction In An Atom May Be Written As E 1 Di S Hso 2 2m Car Dr Wh 1 (80.46 KiB) Viewed 66 times
- The Hamiltonian Associated With The Spin Orbit Interaction In An Atom May Be Written As E 1 Di S Hso 2 2m Car Dr Wh 2 (85.43 KiB) Viewed 66 times
The Hamiltonian associated with the spin-orbit interaction in an atom may be written as e 1 di S. Hso ) (2) 2m car dr where o represents the potential. Given that S ) (3) (ĉ. Š) = lu(J + 1) – L(L + 1) – S(S + 1)]h?, (6) - 73 no alll +1/2)(( + 1)' ) (4) and Ze (5) [3] [1] 471€or (a) i. What do the quantum numbers J, L, and S represent? ii. In terms of L and S what are the possible values of J? (b) Show that the spin-orbit energy shift can be written in the form AEso ACL, S), 1, S) (J(J + 1) – L(L + 1) – S(S+1)] hc 2 where Z4Q2R A(L, S) n3l(l +1/2)(€ + 1) (6) = (7) [4] = Note: ag = 471002/mee? R2 = a2mec/2h e/4nechc = a =
[1] [2] [3] (c) i. What modification to Equation (7) is necessary to make it applicable to hydrogen? ii. Calculate the spin-orbit coupling constant for the 2P levels in hydrogen, i.e., Azp(L, S). iii. Determine the energy splitting between the 22P1/2 and 22P3/2 levels. iv. By considering the M, sublevels, what can be determined about the total energy of the system? What is the physical basis for your answer? (d) The spin-orbit splitting of rubidium (Z = 37) 52P1/2 and 52P3/2 levels is 238 cm-1. i. Determine the corresponding spin-orbit coupling constant for the 52P term in rubidium. ii. Explain why the answer obtained in part (d-i) differs from the value you would find using Equation (7). [2] [2] [2]