Question

Derive the terms of the lowest configuration of the nitrogen atom, 1s22s22p3. For each term, list the values for J.

Answer 1

For notrogen (N) the lowest energy term is again ²P with spin–orbit levels J= 1,0, but now there are three of six possible electrons in the shell so the ground state is ²P₂

If the shell is half-filled then L=0, and hence there is only one value of J (equal to S), which is the lowest energy state. For example in phosphorus the lowest energy state has S=2/2 L=1  for three unpaired electrons in three 2p orbitals. Therefore J=S=2/2 and the ground state is 2S_2/2.

Hund's first rule now states that the ground state term is ²P, which has S = 1. The superscript 3 is the value of the multiplicity = 2S + 1 = 3. The diagram shows the state of this term with M_L = 1 and M_S = 1.