Helium atom

Helium atom

Names
Systematic IUPAC name Helium
Identifiers
CAS Number	7440-59-7 Y
3D model (JSmol)	Interactive image
ChEBI	CHEBI:33681 Y
ChemSpider	22423 Y
EC Number	231-168-5
Gmelin Reference	16294
KEGG	D04420 N
MeSH	Helium
PubChem CID	23987
RTECS number	MH6520000
UN number	1046
InChI InChI=1S/He Y Key: SWQJXJOGLNCZEY-UHFFFAOYSA-N Y
SMILES [He]
Properties
Chemical formula	He
Molar mass	4.00 g·mol−1
Appearance	Colourless gas
Boiling point	−269 °C (−452.20 °F; 4.15 K)
Thermochemistry
Std molar entropy (So298)	126.151-126.155 J K−1 mol−1
Pharmacology
ATC code	V03AN03 (WHO)
Hazards
S-phrases (outdated)	S9
Except where otherwise noted, data are given for materials in their standard state (at 25 °C [77 °F], 100 kPa).
N  (what is YN ?)
Infobox references

A helium atom is an atom of the chemical element helium. Helium is composed of two electrons bound by the electromagnetic force to a nucleus containing two protons along with either one or two neutrons, depending on the isotope, held together by the strong force. Unlike for hydrogen, a closed-form solution to the Schrödinger equation for the helium atom has not been found. However, various approximations, such as the Hartree–Fock method, can be used to estimate the ground state energy and wavefunction of the atom.

The quantum mechanical description of the helium atom is of special interest, because it is the simplest multi-electron system and can be used to understand the concept of quantum entanglement. The Hamiltonian of helium, considered as a three-body system of two electrons and a nucleus and after separating out the centre-of-mass motion, can be written as

where ${\displaystyle \mu ={\frac {mM}{m+M}}}$ is the reduced mass of an electron with respect to the nucleus, ${\displaystyle {\vec {r}}_{1}}$ and ${\displaystyle {\vec {r}}_{2}}$ are the electron-nucleus distance vectors and ${\displaystyle r_{12}=|{\vec {r_{1}}}-{\vec {r_{2}}}|}$. The nuclear charge, ${\displaystyle Z}$ is 2 for helium. In the approximation of an infinitely heavy nucleus, ${\displaystyle M=\infty }$ we have ${\displaystyle \mu =m}$ and the mass polarization term ${\displaystyle {\frac {\hbar ^{2}}{M}}\nabla _{r_{1}}\cdot \nabla _{r_{2}}}$ disappears. In atomic units the Hamiltonian simplifies to