(a) In the LS coupling scheme, the electronic angular momentum states of atoms are specified by four quantum numbers: L,S,J,MJ. What do these four quantum numbers represent? (b) Define the total angular momentum quantum number F, and explain why, in the presence of external fields, F must be a good quantum number. (c) Carbon (Z=6) and lead (Z=82) are both in Group IVB of the periodic table. Carbon has LS coupling, but lead has j j coupling. Why is the angular momentum scheme different for the heavier atom? (d) Use Hund's rules to determine the ground state angular momentum numbers L,S, and J for the following atoms: (i) beryllium (Z=4), (ii) nitrogen (Z=7), (iii) manganese (Z=25), and (iv) iron(Z=26). (e) The Cr4+ ion has an electronic configuration [Ar]3d2. Write down the quantum numbers L,S, and J for the allowed angular momentum states of the 3d4p excited-state configuration of the Cr4+ ion