Atomic Term Symbols
Applying the 'definition' of the term symbol:
results in a ^{2}S_{1/2} atomic term for the ground state of the H atom.
Exciting the single hydrogenic electron to higher orbitals results in different atomic states or 'terms' of the atom. Note that an H atom with the electron in a 3d and 10d orbital both result in ^{2}D_{3/2} and ^{2}D_{5/2} terms, but at different energies.
The lowest electron configuration of He is 1s^{2}.
The ground state of the neutral helium atom is therefore
^{1}S_{0}
In fact, any electron configuration (orbital population) that consists of
any combination of closed shells or subshells will result in this
(totally symmetric ^{1}S_{0} term.
Therefore, in the designation of atomic terms, the contribution from closed subshell
electrons may be neglected.
He(1s^{2})
Ground state term symbol
is ^{1}S_{0}
He(1s^{1}2s^{1}) An Excited State Configuration
Terms:
^{1}S_{0}
,
^{3}S_{1}
{
There is no
^{3}S_{0}
Nor
^{3}S_{-1}
Term
}
B(1s^{2}2s^{2}2p^{1})
Term symbol:
^{2}P_{1/2},
^{2}P_{3/2}
_{The spin orbit splitting is
regular so 2P1/2. is the ground state.
}
C(1s^{2}2s^{2}2p^{2})
Calculate the number of possible electron arrangements in the given
configuration
There are 6!/4!2! = 15 microstates expected
Write down all these possibilities
Decompose this table into terms
What are the atomic state term symbols resulting from the lowest energy configuration of N
(1s^{2} 2s^{2} 2p^{3}) ?
This configuration has 6!/3!3! = 20 microstates
Draw all the possibilities
Tabulate the totals
Assign Terms
What are the atomic state term symbols resulting from the lowest energy configuration of O (1s^{2} 2s^{2} 2p^{4}) ?
Aha! We don't haver to do this because the terms arising from p^{2}
and p^{4} are exactly the same.
Note however the ordering of the J levels is now inverted
Check this with reality
The terms resulting from a single open subshell are tabulated below for your amusement.