Electron atomic and molecular orbitals
In atomic physics and quantum chemistry, electron configuration is the arrangement of
electrons in an atom, molecule, or other physical structure. Like other elementary
particles, the electron is subject to the laws of quantum mechanics, and exhibits both
particle-like and wave-like nature. Formally, the quantum state of a particular electron is
defined by its wave function, a complex-valued function of space and time. According to
the Copenhagen interpretation of quantum mechanics, the position of a particular electron
is not well defined until an act of measurement causes it to be detected. The probability
that the act of measurement will detect the electron at a particular point in space is
proportional to the square of the absolute value of the wavefunction at that point.
Electrons are able to move from one energy level to another by emission or absorption of
a quantum of energy, in the form of a photon. Because of the Pauli exclusion principle,
no more than two electrons may exist in a given atomic orbital; therefore an electron may
only leap to another orbital if there is a vacancy there.
Knowledge of the electron configuration of different atoms is useful in understanding the
structure of the periodic table of elements. The concept is also useful for describing the
chemical bonds that hold atoms together. In bulk materials this same idea helps explain
the peculiar properties of lasers and semiconductors.
Electron configuration in atoms
Summary of the quantum numbers
The state of an electron in an atom is given by four quantum numbers. Three of these are
integers and are properties of the atomic orbital in which it sits (a more thorough
explanation is given in that article).
number denoted allowed range represents
Partly the overall energy of the orbital, and
by extension its general distance from the
quantum n integer, 1 or more
nucleus. In short, the energy level it is in.
azimuthal The orbital's angular momentum, also seen
quantum l integer, 0 to n-1 as the number of nodes in the density plot.
number Otherwise known as its orbital. (s=0, p=1...)
magnetic Determines energy shift of an atomic orbital
integer, -l to +l,
quantum m due to external magnetic field (Zeeman
number effect). Indicates spatial orientation.
Spin is an intrinsic property of the electron
+½ or -½
spin quantum and independent of the other numbers. s and
ms (sometimes called
number l in part determine the electron's magnetic
"up" and "down")
Pauli exclusion principle - No two electrons in one atom can have the same set of these
four quantum numbers
Shells and subshells
Shells and subshells (also called energy levels and sublevels) are defined by the quantum
numbers, not by the distance of its electrons from the nucleus, or even their overall
energy. In large atoms, shells above the second shell overlap (see Aufbau principle).
States with the same value of n are related, and said to lie within the same electron shell.
States with the same value of n and also l are said to lie within the same electron
subshell, and those electrons having the same n and l are called equivalent electrons.
If the states also share the same value of m, they are said to lie in the same atomic orbital.
Because electrons have only two possible spin states, an atomic orbital cannot contain
more than two electrons (Pauli exclusion principle).
A subshell can contain up to 4l + 2 electrons; a shell can contain up to 2n2 electrons;
where n equals the shell number.
Here is the electron configuration for a filled fifth shell:
Shell Subshell Orbitals Electrons
→ 1 type s
n=5 l=0 m=0 → max 2 electrons
→ 3 type p
l=1 m = -1, 0, +1 → max 6 electrons
→ 5 type d
l=2 m = -2, -1, 0, +1, +2 → max 10 electrons
→ 7 type f
l=3 m = -3, -2, -1, 0, +1, +2, +3 → max 14 electrons
m = -4, -3 -2, -1, 0, +1, +2, → 9 type g
l=4 → max 18 electrons
+3, +4 orbitals
Total: max 50
This information can be written as 5s2 5p6 5d10 5f14 5g18 (see below for more details on
Physicists and chemists use a standard notation to describe atomic electron
configurations. In this notation, a subshell is written in the form nxy, where n is the shell
number, x is the subshell label and y is the number of electrons in the subshell. An atom's
subshells are written in order of increasing energy – in other words, the sequence in
which they are filled (see Aufbau principle below).
For instance, ground-state hydrogen has one electron in the s orbital of the first shell, so
its configuration is written 1s1. Lithium has two electrons in the 1s subshell and one in
the (higher-energy) 2s subshell, so its ground-state configuration is written 1s2 2s1.
Phosphorus (atomic number 15), is as follows: 1s2 2s2 2p6 3s2 3p3.
For atoms with many electrons, this notation can become lengthy and so the noble gas
notation is used. It is often abbreviated by noting that the first few subshells are identical
to those of one or another noble gas. Phosphorus, for instance, differs from neon (1s2 2s2
2p6) only by the presence of a third shell. Thus, the electron configuration of neon is
pulled out, and phosphorus is written as follows: [Ne]3s2 3p3.
An even simpler version is simply to quote the number of electrons in each shell, e.g.
(again for phosphorus): 2-8-5.
The orbital labels s, p, d, and f originate from a now-discredited system of categorizing
spectral lines as sharp, principal, diffuse, and fundamental, based on their observed fine
structure. When the first four types of orbitals were described, they were associated with
these spectral line types, but there were no other names. The designation g was derived
by following alphabetical order. Shells with more than five subshells are theoretically
permissible, but this covers all discovered elements. For mnemonic reasons, some call the
s and p orbitals spherical and peripheral.
In the ground state of an atom (the condition in which it is ordinarily found), the electron
configuration generally follows the Aufbau principle. According to this principle,
electrons enter into states in order of the states' increasing energy; i.e., the first electron
goes into the lowest-energy state, the second into the next lowest, and so on. The order in
which the states are filled is as follows:
s p d f g
2 2 3
3 4 5 7
4 6 8 10 13
5 9 11 14 17 21
6 12 15 18 22
7 16 19 23
8 20 24
The order of increasing energy of the subshells can be constructed by going through
downward-leftward diagonals of the table above (also see the diagram at the top of the
page), going from the topmost diagonals to the bottom. The first (topmost) diagonal goes
through 1s; the second diagonal goes through 2s; the third goes through 2p and 3s; the
fourth goes through 3p and 4s; the fifth goes through 3d, 4p, and 5s; and so on. In
general, a subshell that is not "s" is always followed by a "lower" subshell of the next
shell; e.g. 2p is followed by 3s; 3d is followed by 4p, which is followed by 5s, 4f is
followed by 5d, which is followed by 6p, and then 7s. This explains the ordering of the
blocks in the periodic table.
A pair of electrons with identical spins has slightly less energy than a pair of electrons
with opposite spins. Since two electrons in the same orbital must have opposite spins, this
causes electrons to prefer to occupy different orbitals. This preference manifests itself if a
subshell with l > 0 (one that contains more than one orbital) is less than full. For instance,
if a p subshell contains four electrons, two electrons will be forced to occupy one orbital,
but the other two electrons will occupy both of the other orbitals, and their spins will be
equal. This phenomenon is called Hund's rule.
The Aufbau principle can be applied, in a modified form, to the protons and neutrons in
the atomic nucleus (see the shell model of nuclear physics).
This table shows all orbital configurations up to 7s, therefore it covers the simple
electronic configuration for all elements from the periodic table up to Ununbium (element
112) with the exception of Lawrencium (element 103), which would require a 7p orbital.
s (l=0) p (l=1) d (l=2) f (l=3)