Page 259 - Instant notes

Many-electron atoms 245

Hund’s rule arises through a quantum mechanical phenomenon known as spin
correlation in which electrons with the same spin tend to stay further apart from each
other, on average, than electrons with opposite spins.

Atomic term symbols

The electron configuration (ground or excited) of any atom may be succinctly
represented by an appropriate atomic term symbol. It takes the form:
2S+1
{L}
where S is the total spin angular momentum quantum number and {L} is a letter that
signifies the total orbital angular quantum number, L. Thus, when L=0, 1, 2, 3…the
corresponding letter used in the term symbol is S, P, D, F,… Note the comparative
symbolism with the s, p, d, f…letter used to represent electrons in individual atomic
orbitals of orbital momentum quantum number l=0, 1 , 2, 3…, respectively (Topic
G5).
The quantity 2S+1 is known as the multiplicity. Two electrons with paired spin
contribute no net spin angular momentum. Thus for an atom containing no unpaired
electrons, S=0, and the multiplicity is 1 (a singlet state); for an atom containing one
unpaired electron, S=½, and the multiplicity is 2 (a doublet state); for an atom containing
two unpaired electrons, S=1, and the multiplicity is 3 (a triplet state), and so on.
2
For example the ground state electron configuration of He is 1s and has term symbol
1 S. The excited configuration of He in which an electron is promoted from the 1s orbital
1
to the 2s orbital, and spins are opposite in each orbital, also has term symbol S.
However, if the electron spins are parallel in this electron configuration, the term symbol
1
3
3
2
is S. Similarly, the 1s p excited state of He gives rise to term symbols P and P,
depending on whether the electron spins are paired or unpaired. The term symbol for the
2
1
2
ground state of Li (1s 2s ) is S.
In more detailed treatments the term symbol also includes a subscript number after the
symbol for {L} to indicate the value of the total electronic angular momentum (spin and
orbital) quantum number J.