Electron configuration
Learn more about Electron configuration
In atomic physics and quantum chemistry, the electron configuration is the arrangement of electrons in an atom, molecule, or other physical structure (eg, a crystal).
Like other elementary particles, the electron is subject to the laws of quantum mechanics, and exhibits both particle-like and wave-like properties. Formally, the quantum state of a particular electron is defined by its wavefunction, a complex-valued function of space and time. According to the Copenhagen interpretation of quantum mechanics, a particular electron is both "nowhere at all" and "everywhere all at once" 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 jump 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 helps us understand the structure of the periodic table of elements. The concept is also useful for describing the chemical bonds that hold molecules together. And in a macro sense this same idea helps explain the peculiar properties of lasers and semiconductors.
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[edit] Electron configuration in atoms
The discussion below presumes knowledge of material contained at Atomic orbital.
[edit] 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 |
---|---|---|---|
principal quantum number | n | integer, 1 or more | Partly the overall energy of the orbital, and by extension its general distance from the nucleus |
azimuthal quantum number | l | integer, 0 to n-1 | The orbital's angular momentum, also seen as the number of nodes in the density plot |
magnetic quantum number | m | integer, -l to +l, including zero. | Determines energy shift of an atomic orbital due to external magnetic field (Zeeman effect). Indicates spatial orientation. |
spin quantum number | ms | +½ or -½ (sometimes called "up" and "down") | Spin is an intrinsic property of the electron and independent of the other numbers. s and l in part determine the electron's magnetic dipole moment. |
No two electrons in one atom can have the same set of these four quantum numbers (Pauli exclusion principle).
[edit] Shells and subshells
Shells and subshells (also called energy levels and sublevels) are defined by the quantum numbers, and NOT by the distance of its electrons from the nucleus. 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.
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.
[edit] Worked example
Here is the electron configuration for a filled fifth shell:
Shell | Subshell | Orbitals | Electrons | |
n = 5 | l = 0 | m = 0 | → 1 type s orbital | → max 2 electrons |
l = 1 | m = -1, 0, +1 | → 3 type p orbitals | → max 6 electrons | |
l = 2 | m = -2, -1, 0, +1, +2 | → 5 type d orbitals | → max 10 electrons | |
l = 3 | m = -3, -2, -1, 0, +1, +2, +3 | → 7 type f orbitals | → max 14 electrons | |
l = 4 | m = -4, -3 -2, -1, 0, +1, +2, +3, +4 | → 9 type g orbitals | → max 18 electrons | |
Total: max 50 electrons |
This information can be written as 5s^{2} 5p^{6} 5d^{10} 5f^{14} 5g^{18} (see below for more details on notation).
[edit] Notation
Physicists and chemists use a standard notation to describe atomic electron configurations. In this notation, a subshell is written in the form nx^{y}, 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 subshell of the first shell, so its configuration is written 1s^{1}. Lithium has two electrons in the 1s subshell and one in the (higher-energy) 2s subshell, so its ground-state configuration is written 1s^{2} 2s^{1}. Phosphorus (atomic number 15), is as follows: 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{3}.
For atoms with many electrons, this notation can become lengthy. 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 (1s^{2} 2s^{2} 2p^{6}) only by the presence of a third shell. Thus, the electron configuration of neon is pulled out, and phosphorus is written as follows: [Ne]3s^{2} 3p^{3}.
An even simpler version is simply to quote the number of electrons in each shell, e.g. (again for phosphorus): 2-8-5.
[edit] Aufbau principle
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:
<math>s</math> | <math>p</math> | <math>d</math> | <math>f</math> | <math>g</math> | |
---|---|---|---|---|---|
1 | 1 | ||||
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 <math>l>0</math> (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).
[edit] Exceptions in 3d, 4d, 5d
A d subshell that is half-filled or full (ie 5 or 10 electrons) is more stable than the s subshell of the next shell. This is the case because it takes less energy to maintain an electron in a half-filled d subshell than a filled s subshell. For instance, copper (atomic number 29) has a configuration of [Ar]4s^{1} 3d^{10}, not [Ar]4s^{2} 3d^{9} as one would expect by the Aufbau principle. Likewise, chromium (atomic number 24) has a configuration of [Ar]4s^{1} 3d^{5}, not [Ar]4s^{2} 3d^{4}.
Element | Z | Electron configuration | Short electron conf. |
Scandium | 21 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{1} | [Ar] 4s^{2} 3d^{1} |
Titanium | 22 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{2} | [Ar] 4s^{2} 3d^{2} |
Vanadium | 23 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{3} | [Ar] 4s^{2} 3d^{3} |
Chromium | 24 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{5} | [Ar] 4s^{1} 3d^{5} |
Manganese | 25 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{5} | [Ar] 4s^{2} 3d^{5} |
Iron | 26 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{6} | [Ar] 4s^{2} 3d^{6} |
Cobalt | 27 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{7} | [Ar] 4s^{2} 3d^{7} |
Nickel | 28 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{8} | [Ar] 4s^{2} 3d^{8} |
Copper | 29 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{1} 3d^{10} | [Ar] 4s^{1} 3d^{10} |
Zinc | 30 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} | [Ar] 4s^{2} 3d^{10} |
Gallium | 31 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 3d^{10} 4s^{2} 4p^{1} | [Ar] 3d^{10} 4s^{2} 4p^{1} |
This can be most easily understood by stepping through the electron configuration shown at [1]
Period 5 has more exceptions:
Element | Z | Electron configuration | Short electron conf. |
Yttrium | 39 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{2} 4d^{1} | [Kr] 5s^{2} 4d^{1} |
Zirconium | 40 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{2} 4d^{2} | [Kr] 5s^{2} 4d^{2} |
Niobium | 41 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{1} 4d^{4} | [Kr] 5s^{1} 4d^{4} |
Molybdenum | 42 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{1} 4d^{5} | [Kr] 5s^{1} 4d^{5} |
Technetium | 43 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{2} 4d^{5} | [Kr] 5s^{2} 4d^{5} |
Ruthenium | 44 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{1} 4d^{7} | [Kr] 5s^{1} 4d^{7} |
Rhodium | 45 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{1} 4d^{8} | [Kr] 5s^{1} 4d^{8} |
Palladium | 46 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 4d^{10} | [Kr] 4d^{10} |
Silver | 47 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{1} 4d^{10} | [Kr] 5s^{1} 4d^{10} |
Cadmium | 48 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{2} 4d^{10} | [Kr] 5s^{2} 4d^{10} |
Indium | 49 | 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6} 4s^{2} 3d^{10} 4p^{6} 5s^{2} 4d^{10} 5p^{1} | [Kr] 5s^{2} 4d^{10} 5p^{1} |
This can be seen by stepping through the electron configuration shown at [2]
Element | Z | Short electron conf. |
Iridium | 77 | [Xe] 6s^{2} 4f^{14} 5d^{7} |
Platinum | 78 | [Xe] 6s^{1} 4f^{14} 5d^{9} |
Gold | 79 | [Xe] 6s^{1} 4f^{14} 5d^{10} |
Mercury | 80 | [Xe] 6s^{2} 4f^{14} 5d^{10} |
Thallium | 81 | [Xe] 6s^{2} 4f^{14} 5d^{10} 6p^{1} |
This can be seen by stepping through the electron configuration shown at [3]
[edit] Relation to the structure of the periodic table
Electron configuration is intimately related to the structure of the periodic table. The chemical properties of an atom are largely determined by the arrangement of the electrons in its outermost ("valence") shell (although other factors, such as atomic radius, atomic mass, and increased accessibility of additional electronic states also contribute to the chemistry of the elements as atomic size increases).
[edit] Electron configuration in molecules
In molecules, the situation becomes more complex, as each molecule has a different orbital structure. See the molecular orbital article and the linear combination of atomic orbitals method for an introduction and the computational chemistry article for more advanced discussions.
[edit] Electron configuration in solids
In a solid, the electron states become very numerous. They cease to be discrete, and effectively blend together into continuous ranges of possible states (an electron band). The notion of electron configuration ceases to be relevant, and yields to band theory.
[edit] See also
- Atomic electron configuration table
- Periodic table (electron configurations)
- Atomic orbital
- Energy level
- Molecular term symbol
- HOMO/LUMO
- Atompaw Software package for electron configuration calculations
- Pwpaw Software package for electron configuration calculationsaf:Elektronkonfigurasie
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