Written as a determinant, this wavefunction is indeed antisymmetric. If the
determinant were evaluated, it would expand into 24 terms. The electron
configuration, however, is a total of only six alphanumeric characters.
Although the Slater-determinant wavefunction is more complete, the electron
configuration is much more convenient.As we consider larger and larger atoms, electrons start occupying orbitals of
the 2psubshell. It should be recognized that with three possible porbitals,
there are several possible ways of, say, two electrons occupying the various p
orbitals. A statement known as Hund’s ruleindicates that electrons occupy each
degenerate orbital singly before pairing up orbitals with two electrons of op-
posite spin. (The rule was enunciated by Friedrich Hund in 1925 after detailed
consideration of atomic spectra.) In the absence of any other influence, the or-
bitals are still degenerate, so at this point there is no preference about which p
orbitals are singly, then doubly, occupied. Therefore, one specific electron con-
figuration for the ground state of boron can be listed as 1s^22 s^22 px^1 , and a spe-
cific electron configuration for the ground state of carbon can be given as 1s^2
2 s^22 px^12 py^1. If Hund’s rule is assumed, a more general electron configuration
of C can be abbreviated as 1s^22 s^22 p^2.Example 12.7
List two other acceptable ground-state electron configurations for B and C.
Give an unacceptable ground-state electron configuration for C.Solution
Since it does not matter which porbitals are used, the ground state of B can
also be written as 1s^22 s^22 py^1 or 1s^22 s^22 pz^1. For C, the other acceptable elec-
tron configurations are 1s^22 s^22 py^12 pz^1 or 1s^22 s^22 px^12 pz^1. Both of these can
be abbreviated as 1s^22 s^22 p^2. An unacceptable ground-state electron config-
uration might be 1s^22 s^22 px^2 , since this has the electrons paired in a single p
orbital rather than spread out among the degenerate porbitals, as required
by Hund’s rule.The filling of the spin orbitals so far has taken the order 1s,2s,2p.As one
considers the electron configurations of larger atoms, electrons continue to oc-
cupy orbitals through 3sand 3p. But at potassium (Z19), instead of filling
the 3dorbital, the 4sorbital is occupied first. Only after a second electron oc-
cupies the 4sorbital (for calcium) does the 3dsubshell start becoming occu-
pied with electrons.
Why? The naive answer is that the 4sorbital is lower in energy than the 3d
orbital. Since the energies of orbitals in multielectron atoms are determined by
the quantum number as well as the quantum number n, it must be at this
point that the energy E 4 sbecomes less than the energy E 3 d. Actually, this argu-
ment is misleading. The reason that the 4sorbital becomes occupied is that the
totalenergy of the atom is less than it would be if the electron occupied a 3d
orbital.
On the face of it, this seems peculiar. If the 3dorbital were lower in energy,
why shouldn’t it be occupied by an electron first? If it were a hydrogen-like
atom, with only a single electron, then the absolute energy of the orbital would384 CHAPTER 12 Atoms and Molecules