mℓ e
1 ↑
0
-1
s=∑
ms=^12
ℓ=∑
mℓ= 126.6.2 Carbon Ground State
Carbon, withZ= 6 has the 1S and 2S levels filled givingj= 0 as a base. It has two valence 2P
electrons. Hund’s first rule , maximum totals, tells us to couple the two electron spins tos= 1.
This is the symmetric spin state so we’ll need to make the space stateantisymmetric. Hund’s second
rule, maximumℓ, doesn’t play a role because only theℓ= 1 state is antisymmetric. Remember,
adding two P states together, we get totalℓ= 0, 1 ,2. The maximum state is symmetric, the next
antisymmetric, and theℓ= 0 state is again symmetric under interchange. This meansℓ= 1 is the
only option. Since the shell is not half full we couple to the the lowestj=|ℓ−s|= 0. So the ground
state is^3 P 0. The simpler way works with a table.
mℓ e
1 ↑
0 ↑
-1
s=∑
ms= 1
ℓ=∑
mℓ= 1We can take a look at the excited states of carbon to get an appreciation of Hund’s rules. The
following chart shows the states of a carbon atom. For most states, a basis of (1s)^2 (2s)^2 (2p)^1 is
assumed and the state of the sixth electron is given. Some states have other excited electrons and
are indicated by a superscript. Differentjstates are not shown since the splitting is small. Electric
dipole transitions are shown changingℓby one unit.