Explain hund's rule and spectroscopic term of the ground state of an atom

Hund’s rule predicts the stable state of an atom to have large number of unpaired electrons (High spin configuration). The ground state is given by a term, 2S + 1LJ,

Where, the superscript (2S +1) is the maximum multiplicity, L is the total orbital angular momentum and J is the total angular momentum arising out of coupling between the spin and orbital angular momentum.

J will be equal to (L + S) for more than half-filled degenerate orbitals and (L -S) for equal & less than half- filled degenerate orbitals.

ü For carbon with atomic number 6, electronic configuration is 1s22s22p2.

p-orbital is degenerate with three sub orbitals, with different magnetic quantum numbers. The two electros can occupy these orbitals, in many ways, subjected to Pauli’s exclusion principle.

There are three possible states corresponding to three positive ‘L’ values and among them the ground state has the term symbol of 3P2.

Number of unpaired electrons

S

2S + 1

L

J

Term

Ground state

↑↓

0

0

1

2

1

1D1

3P2

2

1

3

1

3P2

2

1

3

0

3

3S3

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