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.
An electron shell is the set of atomic orbitals which share the same principal quantum number, n (the number before the letter in the orbital label): hence the 3s-orbital, the 3p-orbitals and the 3d-orbitals all form part of the third shell. An electron shell can accommodate 2n electrons, ie the first shell can accommodate 2 electrons, the second shell 8 electrons, the third shell 18 electrons, etc.
A subshell is the set of orbitals which have the same orbital label (ie, the same values for n and l). Hence the three 2p-orbitals form a subshell, which can accommodate six electrons, as do the three 4p-orbitals or the five 3d-orbitals. The number of electrons which can be placed in a subshell is given by 2(2l+1): that is two electrons in an "s" subshell, six electrons in a "p" subshell, ten electrons in a "d" subshell and fourteen electrons in an "f" subshell.
The numbers of electrons that can occupy each shell and each subshell arise from the equations of quantum mechanics, in particular the Pauli exclusion principle, which states that no two electrons in the same atom can have the same values of the four quantum numbers.
For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used, noting that the first few subshells are identical to those of one or another of the noble gases. 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. This convention is useful as it is the electrons in the outermost shell which most determine the chemistry of the element.
The order of writing the orbitals is not completely fixed: some sources group all orbitals with the same value of n together, while other sources (as here) follow the order given by Madelung's rule. Hence the electron configuration of iron can be written as [Ar] 3d6 4s2 (keeping the 3d-electrons with the 3s- and 3p-electrons which are implied by the configuration of argon) or as [Ar] 4s2 3d6 (following the Aufbau principle, see below).
The superscript 1 for a singly-occupied orbital is not compulsory. It is quite common to see the letters of the orbital labels (s, p, d, f) written in an italic or slanting typeface, although the International Union of Pure and Applied Chemistry (IUPAC) recommends a normal typeface (as used here). The choice of letters originates from a now-obsolete system of categorizing spectral lines as "sharp", "principal", "diffuse" and "fine", based on their observed fine structure: their modern usage indicates orbitals with an . azimuthal quantum number, l, of 0, 1, 2 or 3 respectively. After "f", the sequence continues alphabetically "g", "h", "i"… (l = 4, 5, 6…), although orbitals of these types are rarely required.
The electron configurations of molecules are written in a similar way, except that molecular orbital labels are used instead of atomic orbital labels (see below).
The following year, E. C. Stoner incorporated Sommerfeld's third quantum number into the description of electron shells, and correctly predicted the shell structure of sulfur to be 2.8.6. However neither Bohr's system nor Stoner's could correctly describe the changes in atomic spectra in a magnetic field (the Zeeman effect).
Bohr was well aware of this shortcoming (and others), and had written to his friend Wolfgang Pauli to ask for his help in saving quantum theory (the system now known as "old quantum theory"). Pauli realized that the Zeeman effect must be due only to the outermost electrons of the atom, and was able to reproduce Stoner's shell structure, but with the correct structure of subshells, by his inclusion of a fourth quantum number and his exclusion principle (1925):
It should be forbidden for more than one electron with the same value of the main quantum number n to have the same value for the other three quantum numbers k [l], j [ml] and m [ms].The Schrödinger equation, published in 1926, gave three of the four quantum numbers as a direct consequence of its solution for the hydrogen atom: this solution yields the atomic orbitals which are shown today in textbooks of chemistry (and above). The examination of atomic spectra allowed the electron configurations of atoms to be determined experimentally, and led to an empirical rule (known as Madelung's rule (1936), see below) for the order in which atomic orbitals are filled with electrons.
The fact that the Aufbau principle is based on an approximation can be seen from the fact that there is an almost-fixed filling order at all, that, within a given shell, the s-orbitals are always filled before the p-orbitals. In a hydrogen-like atom, which only has one electron, the s-orbitals and the p-orbitals of the same shell have exactly the same energy (in the absence of an external electric or magnetic field).
The apparent paradox arises when electrons are removed from the transition metal atoms to form ions. The first electrons to be ionized come not from the 3d-orbital, as one would expect if it were "higher in energy", but from the 4s-orbital. The same is true when chemical compounds are formed. Chromium hexacarbonyl can be described as a chromium atom (not ion, it is in the oxidation state 0) surrounded by six carbon monoxide ligands: it is diamagnetic, and the electron configuration of the central chromium atom is described as 3d, ie the electron which was in the 4s-orbital in the free atom has passed into a 3d-orbital on forming the compound. This interchange of electrons between 4s and 3d is universal among the first series of the transition metals.
The phenomenon is only paradoxical if it is assumed that the energies of atomic orbitals are fixed and unaffected by the presence of electrons in other orbitals. If that were the case, the 3d-orbital would have the same energy as the 3p-orbital, as it does in hydrogen, yet it clearly doesn't. There is no special reason why the Fe ion should have the same electron configuration as the chromium atom, given that iron has two more protons in its nucleus than chromium and that the chemistry of the two species is very different. When care is taken to compare "like with like", the paradox disappears.
|Period 5||Period 6||Period 7|
|Element||Z||Electron Configuration||Element||Z||Electron Configuration||Element||Z||Electron Configuration|
|Yttrium||39||[Kr] 5s2 4d1||Lanthanum||57||[Xe] 6s2 5d1||Actinium||89||[Rn] 7s2 6d1|
|Cerium||58||[Xe] 6s2 4f1 5d1||Thorium||90||[Rn] 7s2 6d2|
|Praseodymium||59||[Xe] 6s2 4f3||Protactinium||91||[Rn] 7s2 5f2 6d1|
|Neodymium||60||[Xe] 6s2 4f4||Uranium||92||[Rn] 7s2 5f3 6d1|
|Promethium||61||[Xe] 6s2 4f5||Neptunium||93||[Rn] 7s2 5f4 6d1|
|Samarium||62||[Xe] 6s2 4f6||Plutonium||94||[Rn] 7s2 5f6|
|Europium||63||[Xe] 6s2 4f7||Americium||95||[Rn] 7s2 5f7|
|Gadolinium||64||[Xe] 6s2 4f7 5d1||Curium||96||[Rn] 7s2 5f7 6d1|
|Terbium||65||[Xe] 6s2 4f9||Berkelium||97||[Rn] 7s2 5f9|
|Zirconium||40||[Kr] 5s2 4d2||Hafnium||72||[Xe] 6s2 4f14 5d2|
|Niobium||41||[Kr] 5s1 4d4||Tantalium||73||[Xe] 6s2 4f14 5d3|
|Molybdenum||42||[Kr] 5s1 4d5||Tungsten||74||[Xe] 6s2 4f14 5d4|
|Technetium||43||[Kr] 5s2 4d5||Rhenium||75||[Xe] 6s2 4f14 5d5|
|Ruthenium||44||[Kr] 5s1 4d7||Osmium||76||[Xe] 6s2 4f14 5d6|
|Rhodium||45||[Kr] 5s1 4d8||Iridium||77||[Xe] 6s2 4f14 5d7|
|Palladium||46||[Kr] 4d10||Platinum||78||[Xe] 6s1 4f14 5d9|
|Silver||47||[Kr] 5s1 4d10||Gold||79||[Xe] 6s1 4f14 5d10|
|Cadmium||48||[Kr] 5s2 4d10||Mercury||80||[Xe] 6s2 4f14 5d10|
|Indium||49||[Kr] 5s2 4d10 5p1||Thallium||81||[Xe] 6s2 4f14 5d10 6p1|
This approach is taken further in calculational chemistry, which typically attempts to make quantitative estimates of chemical properties. For many years, most such calculations relied upon the "linear combination of atomic orbitals" (LCAO) approximation, using ever larger an more complex basis set of atomic orbitals as the starting point. The last step in such a calculation is the assignment of electrons among the molecular orbitals according to the Aufbau principle. Not all methods in calculational chemistry rely on electron configuration: density functional theory (DFT) is an important example of a method which discards the model.
A fundamental application of electron configurations is in the interpretation of atomic spectra. In this case, it is necessary to convert the electron configuration into one or more term symbols, which describe the different energy levels available to an atom. Term symbols can be calculated for any electron configuration, not just the ground-state configuration listed in tables, although not all the energy levels are observed in practice. It is through the analysis of atomic spectra that the ground-state electron configurations of the elements were experimentally determined.