Question

Use the full microstates method to find all the possible term symbols and predict an
order from lowest to highest energy for the following elements: nitrogen, oxygen,
vanadium, niobium, bismuth, and livermorium. (Hint: consider if there are any
insights that the organization of the periodic table can give to simplify this problem.)
What practical insights or shortcuts may be used to predict the term symbols of other
elements? Give at least three examples of elements and term symbols that the work above would account for.
(Physical Chemistry)

Answer 1

Atoms	Electronic configuration	Number of unpaired electron(n)	S=n/2	Spin multiplicity s=2S + 1	L(symbol)	J = ІL+SІ.... ІL-SІ	2s+1LJ
nitrogen	[He] 2s22p3	3	3/2	4	0(S)	3/2	4S3/2
oxygen	[He] 2s22p4	2	1	3	1(P)	2,1,0	3P2,3P1,3P0
vanadium	[Ar] 4S23d3	3	3/2	4	3(F)	9/2,7/2,5/2,3/2	4F9/2,4F7/2,4F5/2,4F3/2
niobium	[Kr] 4d4 5s1	4	2	5	2(D)	4,3,2,1,0	5D4,5D3,5D2,5D1,5D0
bismuth	[Xe] 4f14 5d10 6s2 6p3	3	3/2	4	0(S)	3/2	4S3/2
livermorium	[Rn] 5f14 6d10 7s2 7p4	2	1	3	1(P)	2,1,0	3P2,3P1,3P0

Note

1) Atoms having same outer electronic configuration have same term symbols( nitrogen and

    bismuth)

2) Competely and half filled electronic configuration have L value zero and hence S symbol

3)when subshell is more than half filled Higher term symbol is ground state and for less than half

    filled lower value id ground state see marked in red

4) L should be calculated as summation of orientation for subshell

Eg: for P² L Value is 1 and value is always positive

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