P460 - atoms III1 More Energy Levels in Atoms If all (both) electrons are at the same n. Use Hund’s Rules (in order of importance) minimize ee repulsion by maximizing ee separation --> “exchange force” where antisymmetric spatial wavefunction has largest spatial separation > maximum S has minimum E different L -> different wavefunctions -> different effective Z (radial distributions) > maximum L has minimum E > minimum J has minimum E unless subshell >1/2 filled and then > minimum J has maximum E

P460 - atoms III2 3d4p S=0,1 L=1,2,3 S=0 S=1 L=1 J=1 L=2 J=2 L=3 J=3 L=1 L=2 L=3 J=2 J=1 J=0 J=3 J=2 J=1 J=4 J=3 J=2 J splitting Lande interval rule

P460 - atoms III3 Zeeman Effect:External B Field Energy shift depends on m j and removes any remaining degeneracy. Now two fields (internal and external) and details of splitting depends on relative strengths Unless S=0, the magnetic moment and the total angular momentum are not in the same direction (and aren’t in B direction). For weak external field, manipulating the dot products (angles, homework) gives B=0 B>0

P460 - atoms III4 Zeeman Effect:External B Field Assume again that weak B field (did strong field in Ch. 8) B field off --> 1 photon energy B field on --> 6 photon energies (with their energy depending on the g facor and on the B field One of the first indicators that the electron had intrinsic angular momentum s=1/2 B=0 B>0