I'm certainly missing something here. The problem is to find the ground state L and S for Gd, with a configuration given as [Xe]6s^2,4f^7,5d^1. I start by calculating Smax. I'm figuring you get 1/2 for the 5d^1 electron, plus (since the f level has room for 14 electrons, all 7 can have +1/2 spin) 7/2 give Smax = 4. How do I get L? It would seem that Lmax would be 4 for the 5d^1 electron and 3 for the others, making a total of 7. The book says it should be 2, and I can't see how, for example, the Pauli exclusion principle should get me there. Any help would be appreciated - I really want to understand the concept as much as deal with this problem. Thanks.