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Many-electron atoms 243

no more than two electrons can occupy a given atomic orbital (or molecular orbital), and
when two electrons do occupy one orbital their spins must be paired.

The exclusion principle is a key feature in the derivation of electron configuration
through the Aufbau (or building-up) principle.

Electron configuration

The distribution of electrons into individual atomic orbitals within the orbital
approximation is called the electron configuration of the atom. The electron
distribution of lowest energy is called the ground state configuration. All electron
distributions of higher energy are called excited state configurations. For example, the
ground state of a hydrogen atom consists of a single electron in a 1s orbital, so its
1
configuration is written 1s . The configuration of the ground state of the helium atom is
2
written 1s . The first excited state of helium requires energy to promote one of the 1s
1
1
electrons into the 2s orbital and the configuration is 1s 2s .
Aufbau principle

The procedure used to determine the ground state configurations of many-electron
atoms by sequentially filling up individual atomic orbitals is called the Aufbau (or
building-up) principle. Building-up starts with the lowest energy orbital first and
continues until all electrons in the atom (equal to the atomic number, Z) have been
assigned to an orbital. The order of occupation of sub-shells is 1s 2s 2p 3s 3p 4s 3d 4p 5s
4d 5p 6s 5d 4f 6p….
The order of occupation is approximately the order of energy of the individual orbitals
as determined by principal shell and penetration. The ability of the 4s orbital to
penetrate the inner shells lowers its energy below that of the 3d orbitals. The same occurs
for the 5s orbital.
Each orbital within a sub-shell may accommodate a maximum of two electrons (Pauli
exclusion principle). An s sub-shell contains one s orbital and is complete when it
contains two electrons. A p sub-shell contains three degenerate p orbitals and is complete
when it contains six electrons. A d sub-shell contains five degenerate d orbitals and is
complete when it contains ten electrons (see Topic G5, Table 1).
As an example of the Aufbau principle, consider the six electrons of the carbon atom
(Z=6). Two electrons fill the 1s orbital, two electrons fill the 2s orbital and the last two
2
2
2
2
electrons occupy the 2p orbitals. The configuration is therefore 1s 2s 2p . Since 1s
represents a filled principal quantum shell, equivalent to a He atom, the configuration
2
2
can also be written as [He]2s 2p . A filled principal shell is called a closed shell.
Electrons which occupy orbitals in the outermost principal shell (called the valence shell)
are called valence electrons; electrons which occupy closed inner shells are called core
electrons. Carbon has four valence electrons occupying 2s and 2p orbitals. Sodium
1
2
2
6
1
(Z=11) has an electron configuration 1s 2s 2p 3s (also written as [Ne]3s ) and has one
valence electron. All alkali metals have similar configurations of a single s electron