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The approximate order of filling of atomic orbitals, following the arrows from 1s to 7p. (After 7p the order includes subshells outside the range of the diagram, starting with 8s.) The principle works very well (for the ground states of the atoms) for the known 118 elements, although it is sometimes slightly wrong.
The direction of the red arrow indicates the order of state filling. Although it is sometimes stated that all the electrons in a shell have the same energy, this is an approximation. However, the electrons in one subshell do have exactly the same level of energy, with later subshells having more energy per electron than earlier ones. This ...
The rule then predicts the electron configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 9 4s 2, abbreviated [Ar] 3d 9 4s 2 where [Ar] denotes the configuration of argon, the preceding noble gas. However, the measured electron configuration of the copper atom is [Ar] 3d 10 4s 1. By filling the 3d subshell, copper can be in a lower energy state.
The electron will eventually lose energy (by releasing a photon) and drop into the lower orbital. Thus, electrons fill orbitals in the order specified by the energy sequence given above. This behavior is responsible for the structure of the periodic table. The table may be divided into several rows (called 'periods'), numbered starting with 1 ...
As an approximate rule, electron configurations are given by the Aufbau principle and the Madelung rule. However there are numerous exceptions; for example the lightest exception is chromium, which would be predicted to have the configuration 1s 2 2s 2 2p 6 3s 2 3p 6 3d 4 4s 2 , written as [Ar] 3d 4 4s 2 , but whose actual configuration given ...
Grayed out electron numbers indicate subshells filled to their maximum. Bracketed noble gas symbols on the left represent inner configurations that are the same in each period. Written out, these are: He, 2, helium : 1s 2 Ne, 10, neon : 1s 2 2s 2 2p 6 Ar, 18, argon : 1s 2 2s 2 2p 6 3s 2 3p 6 Kr, 36, krypton : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 ...
Another way to predict magic (and semi-magic) numbers is by laying out the idealized filling order (with spin–orbit splitting but energy levels not overlapping). For consistency, s is split into j = 1 / 2 and j = − 1 / 2 components with 2 and 0 members respectively. Taking the leftmost and rightmost total counts within ...
The single-electron Schrödinger equation is solved for an electron in a lattice-periodic potential, giving Bloch electrons as solutions = (), where k is called the wavevector. For each value of k , there are multiple solutions to the Schrödinger equation labelled by n , the band index, which simply numbers the energy bands.