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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Electron configuration | 3/6 | https://en.wikipedia.org/wiki/Electron_configuration | reference | science, encyclopedia | 2026-05-05T10:52:21.981173+00:00 | kb-cron |
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 that 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.
== Atoms: Aufbau principle and Madelung rule ==
The aufbau principle (from the German Aufbau, "building up, construction") was an important part of Bohr's original concept of electron configuration. It may be stated as:
a maximum of two electrons are put into orbitals in the order of increasing orbital energy: the lowest-energy subshells are filled before electrons are placed in higher-energy orbitals. The principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong. The modern form of the aufbau principle describes an order of orbital energies given by Madelung's rule (or Klechkowski's rule). This rule was first stated by Charles Janet in 1929, rediscovered by Erwin Madelung in 1936, and later given a theoretical justification by V. M. Klechkowski: Subshells are filled in the order of increasing n + l. Where two subshells have the same value of n + l, they are filled in order of increasing n. This gives the following order for filling the orbitals:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, (8s, 5g, 6f, 7d, 8p, and 9s) In this list the subshells in parentheses are not occupied in the ground state of the heaviest atom now known (Og, Z = 118). The aufbau principle can be applied, in a modified form, to the protons and neutrons in the atomic nucleus, as in the shell model of nuclear physics and nuclear chemistry.
=== Periodic table ===
The form of the periodic table is closely related to the atomic electron configuration for each element. For example, all the elements of group 2 (the table's second column) have an electron configuration of [E] ns2 (where [E] is a noble gas configuration), and have notable similarities in their chemical properties. The periodicity of the periodic table in terms of periodic table blocks is due to the number of electrons (2, 6, 10, and 14) needed to fill s, p, d, and f subshells. These blocks appear as the rectangular sections of the periodic table. The single exception is helium, which despite being an s-block atom is conventionally placed with the other noble gasses in the p-block due to its chemical inertness, a consequence of its full outer shell (though there is discussion in the contemporary literature on whether this exception should be retained). The electrons in the valence (outermost) shell largely determine each element's chemical properties. The similarities in the chemical properties were remarked on more than a century before the idea of electron configuration.
=== Shortcomings of the aufbau principle === The aufbau principle rests on a fundamental postulate that the order of orbital energies is fixed, both for a given element and between different elements; in both cases this is only approximately true. It considers atomic orbitals as "boxes" of fixed energy into which can be placed two electrons and no more. However, the energy of an electron "in" an atomic orbital depends on the energies of all the other electrons of the atom (or ion, or molecule, etc.). There are no "one-electron solutions" for systems of more than one electron, only a set of many-electron solutions that cannot be calculated exactly (although there are mathematical approximations available, such as the Hartree–Fock method). 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-orbital is always filled before the p-orbitals. In a hydrogen-like atom, which only has one electron, calculations indicate that the s-orbital and the p-orbitals of the same shell have exactly the same energy, which in reality is a very good approximation in the absence of external electromagnetic fields. (However, in a real hydrogen atom, the energy levels are slightly split by the magnetic field of the nucleus, and by the quantum electrodynamic effects of the Lamb shift.)