SOLVED:(a) Show that the following formulae summarize the Hund's rules for a shell of angular momentum l containing n electrons: S=1 / 2[(2 l+1)-|2 l+1-n|] L=S[2 l+1-n] J=|2 l-n| S (b) For a given L S -multiplet, verify that (2 L+1)(2 S+1)=∑|L-S|^|L+S|(2 J+1) (c) Find the ground state of (i) Eu^2+ in the configuration 4 f^7 5 s^2 p^6 (ii) Dy^3+ in the configuration 4 f^9 5 s^2 p^6 (iii) Tm^3+ in the configuration 4 f^12 5 s^2 p^6

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