Editing Atomic radius (section)

==Definitions==
<!--{{atomic radius}}-->
Widely used definitions of atomic radius include:

* [[Van der Waals radius]]: In the simplest definition, half the minimum distance between the nuclei of two atoms of the element that are not otherwise bound by covalent or metallic interactions.<ref name="Pauling1945">
{{cite book
 |last1=Pauling  | first1=L.
 |year=1945<!--LoC says 1940, but everywhere else says 1945-->
 |title=The Nature of the Chemical Bond
 |edition=2nd
 |publisher=[[Cornell University Press]]
 |lccn=42034474
}}</ref>  The Van der Waals radius may be defined even for elements (such as metals) in which Van der Waals forces are dominated by other interactions.  Because [[Van der Waals force|Van der Waals interactions arise through quantum fluctuations of the atomic polarisation]], the polarisability (which can usually be measured or calculated more easily) may be used to define the Van der Waals radius indirectly.<ref name="Federov2018">
{{cite journal
 |last1=Federov |first1=Dmitry V.
 |last2=Sadhukhan |first2=Mainak
 |last3=Stöhr |first3=Martin
 |last4=Tkatchenko |first4=Alexandre
 |year=2018
 |title=Quantum-Mechanical Relation between Atomic Dipole Polarizability and the van der Waals Radius
 |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.121.183401
 |journal=[[Physical Review Letters]]
 |volume=121 |issue=18 |pages=183401
 |access-date=9 May 2021
 |doi=10.1103/PhysRevLett.121.183401
|pmid=30444421
 |arxiv=1803.11507
 |bibcode=2018PhRvL.121r3401F
 |s2cid=53564141
 }}</ref>

* [[Ionic radius]]: the nominal radius of the ions of an element in a specific ionization state, deduced from the spacing of atomic nuclei in crystalline salts that include that ion. In principle, the spacing between two adjacent oppositely charged ions (the [[bond length|length]] of the [[ionic bond]] between them) should equal the sum of their ionic radii.<ref name="Pauling1945"/>
* [[Covalent radius]]: the nominal radius of the atoms of an element when [[covalent bond|covalently bound]] to other atoms, as deduced from the separation between the atomic nuclei in molecules. In principle, the distance between two atoms that are bound to each other in a molecule (the length of that covalent bond) should equal the sum of their covalent radii.<ref name="Pauling1945"/>
* [[Metallic radius]]: the nominal radius of atoms of an element when joined to other atoms by [[metallic bond]]s.{{citation needed|date=August 2009}}
* [[Bohr radius]]: the radius of the lowest-energy electron orbit predicted by [[Bohr model]] of the atom (1913).<ref name="bohrI">
{{cite journal
 |last=Bohr |first=N.
 |year=1913
 |title=On the Constitution of Atoms and Molecules, Part I. – Binding of Electrons by Positive Nuclei
 |url=http://web.ihep.su/dbserv/compas/src/bohr13/eng.pdf |archive-url=https://web.archive.org/web/20110902020206/http://web.ihep.su/dbserv/compas/src/bohr13/eng.pdf |archive-date=2011-09-02 |url-status=live
 |journal=[[Philosophical Magazine]]
 |series=6 |volume=26 |issue=151 |pages=1–24
 |access-date=8 June 2011
 |doi=10.1080/14786441308634955 |bibcode=1913PMag...26....1B
}}</ref><ref name="bohrII">
{{cite journal
 |last=Bohr |first=N.
 |year=1913
 |title=On the Constitution of Atoms and Molecules, Part II. – Systems containing only a Single Nucleus
 |url=http://web.ihep.su/dbserv/compas/src/bohr13b/eng.pdf |archive-url=https://web.archive.org/web/20081209111729/http://web.ihep.su/dbserv/compas/src/bohr13b/eng.pdf |archive-date=2008-12-09 |url-status=live
 |journal=[[Philosophical Magazine]]
 |series=6 |volume=26 |issue=153 |pages=476–502
 |access-date=8 June 2011
 |doi=10.1080/14786441308634993 |bibcode=1913PMag...26..476B
}}</ref>  It is only applicable to [[hydrogen-like atom|atoms and ions with a single electron]], such as [[hydrogen]], singly ionized [[helium]], and [[positronium]].  Although the model itself is now obsolete, the Bohr radius for the hydrogen atom is still regarded as an important physical constant, because it is equivalent to the quantum-mechanical most probable distance of the electron from the nucleus.