Editing Pauli exclusion principle (section)

=== Atoms ===
The Pauli exclusion principle helps explain a wide variety of physical phenomena. One particularly important consequence of the principle is the elaborate [[electron configuration|electron shell structure]] of atoms and the way atoms share electrons, explaining the variety of chemical elements and their chemical combinations. An [[electric charge|electrically neutral]] atom contains bound electrons equal in number to the protons in the [[atomic nucleus|nucleus]]. Electrons, being fermions, cannot occupy the same quantum state as other electrons, so electrons have to "stack" within an atom, i.e. have different spins while at the same electron orbital as described below.

An example is the neutral [[helium atom]] (He), which has two bound electrons, both of which can occupy the lowest-energy ([[Electron shell|1s]]) states by acquiring opposite spin; as spin is part of the quantum state of the electron, the two electrons are in different quantum states and do not violate the Pauli principle. However, the spin can take only two different values ([[eigenvalue]]s). In a [[lithium]] atom (Li), with three bound electrons, the third electron cannot reside in a 1s state and must occupy a higher-energy state instead. The lowest available state is 2s, so that the [[ground state]] of Li is 1s<sup>2</sup>2s. Similarly, successively larger elements must have shells of successively higher energy. The chemical properties of an element largely depend on the number of electrons in the outermost shell; atoms with different numbers of occupied electron shells but the same number of electrons in the outermost shell have similar properties, which gives rise to the [[periodic table|periodic table of the elements]].<ref name=Griffiths2004>{{citation| author=Griffiths, David J.|title=Introduction to Quantum Mechanics (2nd ed.) | publisher=Prentice Hall |year=2004 |isbn= 0-13-111892-7}}</ref>{{rp|214–218}}

To test the Pauli exclusion principle for the helium atom, Gordon Drake<ref>{{cite journal | last = Drake | first = G.W.F.| year = 1989| title = Predicted energy shifts for "paronic" Helium| url = https://scholar.uwindsor.ca/physicspub/85| journal = Phys. Rev. A| volume = 39 | issue = 2 
| pages = 897–899 | doi =10.1103/PhysRevA.39.897| pmid = 9901315| bibcode = 1989PhRvA..39..897D| s2cid = 35775478}}</ref> carried out very precise calculations for hypothetical states of the He atom that violate it, which are called '''paronic states'''. Later, K. Deilamian et al.<ref>{{cite journal | last = Deilamian | first = K.|display-authors=etal|year = 1995 | title = Search for small violations of the symmetrization postulate in an excited state of Helium| journal = Phys. Rev. Lett.| volume = 74 | issue = 24| pages = 4787–4790 | doi=10.1103/PhysRevLett.74.4787| pmid = 10058599| bibcode = 1995PhRvL..74.4787D}}</ref> used an atomic beam spectrometer to search for the paronic state 1s2s <sup>1</sup>S<sub>0</sub> calculated by Drake. The search was unsuccessful and showed that the statistical weight of this paronic state has an upper limit of {{val|5|e=-6}}. (The exclusion principle implies a weight of zero.)