2. Consider the atom V (Vanadium) with 3 open-shell 3d electrons in the LAr4s 3d
ID: 699084 • Letter: 2
Question
2. Consider the atom V (Vanadium) with 3 open-shell 3d electrons in the LAr4s 3d configuration (assume that the 4s level is filled with two electrons). Determine the microstate of highest Ms with highest ML value. Determine the corresponding S and L and the allowed J values and indicate the degeneracy and term value of each multiplet. Next consider the microstate with the highest possible ML value of highest Ms. Again determine the corresponding L and S and the allowed J values and indicate the order the states you found according to energy. Clearly indicate which energy levels are close in energy and which are more widely separated. How many microstates have you found in total? How many microstates are there in total in the [Ar4s d configuration?Explanation / Answer
The ground state electronic configuration of vanadium (V) = [Ar] 4s23d3
First of all, the term symbol corresponding to the ground state of V = (2S+1)LJ
Here, S = 3*1/2 = 3/2
Therefore, the spin multiplicity = 2S+1 = 2*3/2 + 1 = 4 (quartet)
The L value = +2+1+0 = 3, which corresponds to the term 'F'.
The J value for the given configuration = L - S = 3 - 3/2 = 3/2 (since less than half filled configuration)
Therefore, the term symbol corresponding to the ground state of V = 4F3/2
The no. of possible microstates for d3 configuration = 10c3 = 120
The microstate with highest MS value = 4, for which the ML value = 3/2
The corresponding S value = 3/2, L = 3 and allowed J values = L + S to L - S, i.e. from (3+3/2) to (3-3/2) = +9/2 to 3/2
The next microstate with highest MS value = 2. for which the ML value = 3/2
The corresponding S value = 1/2, L = 2 and allowed J values = (2+1/2) to (2-1/2) = 5/2 to 3/2
The states with less difference in J value will be closer in energy, whereas the states with high difference in J value will be widely separated.
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