Editing Atomic radius

{{Short description|Measure of the size of an atom}}
[[File:Helium atom QM.svg|180px|thumb|right|Diagram of a helium atom, showing the electron probability density as shades of gray.]]
The '''atomic radius''' of a [[chemical element]] is a measure of the size of its [[atom]], usually the mean or typical distance from the center of the [[Atomic nucleus|nucleus]] to the outermost isolated [[electron]].  Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are:  [[Van der Waals radius]], [[ionic radius]], [[metallic radius]]  and [[covalent radius]]. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions.

Depending on the definition, the term may apply to atoms in [[condensed matter]], [[covalent bonding|covalently bonding]] in [[molecule]]s, or in [[ionization|ionized]] and [[excited state]]s; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context.<ref>
{{cite book
 |last1=Cotton |first1=F. A.
 |last2=Wilkinson |first2=G.
 |year=1988
 |title=Advanced Inorganic Chemistry
 |page=1385
 |edition=5th
 |publisher=[[John Wiley & Sons|Wiley]]
 |isbn=978-0-471-84997-1
}}</ref>

Electrons do not have definite orbits nor sharply defined ranges. Rather, their positions must be described as [[probability distribution]]s that taper off gradually as one moves away from the nucleus, without a sharp cutoff; these are referred to as [[atomic orbital]]s or electron clouds. Moreover, in condensed matter and molecules, the electron clouds of the atoms usually overlap to some extent, and some of the electrons may roam over a large region encompassing two or more atoms.

Under most definitions the radii of isolated neutral atoms range between 30 and 300 [[picometre|pm]] ([[Orders of magnitude (numbers)#10.E2.88.9212|trillionths]] of a meter), or between 0.3 and 3 [[ångström]]s. Therefore, the radius of an atom is more than 10,000 times the [[nuclear radius|radius of its nucleus]] (1–10 [[femtometre|fm]]),<ref name=Basdevant>
{{cite book
 |last1=Basdevant |first1=J.-L.
 |last2=Rich |first2=J.
 |last3=Spiro |first3=M.
 |year=2005
 |title=Fundamentals in Nuclear Physics
 |url=https://books.google.com/books?id=OFx7P9mgC9oC&q=helium+%22nuclear+structure%22&pg=PA375
 |page=13, fig 1.1
 |publisher=[[Springer (publisher)|Springer]]
 |isbn=978-0-387-01672-6
}}</ref> and less than 1/1000 of the [[wavelength]] of visible [[light]] (400–700 [[nanometre|nm]]).

[[File:Ethanol-3D-vdW.png|180px|right|thumb|The approximate shape of a molecule of [[ethanol]], CH<sub>3</sub>CH<sub>2</sub>OH. Each atom is modeled by a sphere with the element's [[Van der Waals radius]].]]
For many purposes, atoms can be modeled as spheres. This is only a crude approximation, but it can provide quantitative explanations and predictions for many phenomena, such as the [[density]] of liquids and solids, the [[diffusion]] of fluids through [[molecular sieves]], the arrangement of atoms and ions in [[crystal]]s, and the [[space-filling model|size and shape of molecules]].{{citation needed|date=August 2009}}

==History==

The first to estimate the radius of an atom was [[Johann Chrysostom Magnenus]] in 1646. He was at [[Mass (liturgy)|Mass]] and noticed the smell of incense permeating the church. He knew the size of the incense and estimated the size of the church. He presumed that he could detect the incense if one atom was in each nostril. He also presumed that the incense was distributed homogenously throughout the church. With these assumptions he was able to estimate the size of an atom to be about 10 to the power of −24 cubic metres. (The units he used have been converted to metric to make comparisons with later estimates easier.) Taking the cube root this gives an estimate of the atomic radius to be about 10 to the power of −8 metres. This is somewhat larger than current estimates but given the assumptions made in the calculation is very good. These calculations were published in his work ''Democritus reviviscens sive de atomis''.   

The concept of atomic radius was preceded in the 19th century by the concept of atomic volume, a relative measure of how much space would on average an atom occupy in a given solid or liquid material.<ref>{{Cite book |last=Knight |first=Charles |url=https://books.google.com/books?id=vHdBAAAAcAAJ&pg=PA711 |title=The English Cyclopaedia: A New Dictionary of Universal Knowledge |date=1859 |publisher=Bradbury and Evans |language=en}}</ref> By the end of the century this term was also used in an absolute sense, as a [[molar volume]] divided by [[Avogadro constant]].<ref>{{Cite journal |last=Fessenden |first=Reginald A. |author-link=Reginald Fessenden |date=1892-07-22 |title=The Laws and Nature of Cohesion |url=https://books.google.com/books?id=7EAwLffl2WEC&pg=PA49 |journal=Science |language=en |volume=ns-20 |issue=494 |pages=48–52 |doi=10.1126/science.ns-20.494.48.b |issn=0036-8075|url-access=subscription }}</ref> Such a volume is different for different crystalline forms even of the same compound,<ref>{{Cite book |last=Watts |first=Henry |url=https://books.google.com/books?id=noPIn5j1dAMC&pg=PA432 |title=A Dictionary of chemistry and the allied branches of other sciences v. 3, 1882 |date=1882 |publisher=Longmans, Green & Company |language=en}}</ref> but physicists used it for rough, order-of-magnitude estimates of the atomic size, getting 10<sup>−8</sup>–10<sup>−7</sup> cm for copper.<ref>{{Cite book |url=https://books.google.com/books?id=81pPJyOD7dwC&pg=PA157 |title=Electrical World |date=1893 |publisher=McGraw-Hill |language=en}}</ref>

The earliest estimates of the atomic size was made by opticians in the 1830s, particularly [[Augustin-Louis Cauchy|Cauchy]],<ref name=":0">{{Cite journal |last=Fessenden |first=Reginald Aubrey |author-link=Reginald Fessenden |date=February 1900 |title=A Determination of the Nature of the Electric and Magnetic Quantities and of the Density and Elasticity of the Ether, II |url=https://link.aps.org/doi/10.1103/PhysRevSeriesI.10.83 |journal=Physical Review |series=Series I |language=en |volume=10 |issue=2 |pages=83–115 |doi=10.1103/PhysRevSeriesI.10.83 |issn=1536-6065}}</ref><ref>{{Cite journal |last=Thomson |first=W. |author-link=Lord Kelvin |date=1870-07-01 |title=On the size of atoms |url=https://books.google.com/books?id=NQ4zmCTZcR4C&pg=PA38 |journal=American Journal of Science |language=en |volume=s2-50 |issue=148 |pages=38–44 |doi=10.2475/ajs.s2-50.148.38|url-access=subscription }}</ref> who developed models of light [[Dispersion (optics)|dispersion]] assuming a lattice of connected "molecules".<ref>{{Cite book |last=Darrigol |first=Olivier |url=https://books.google.com/books?id=ImM62wvWE_cC&pg=PA247 |title=A History of Optics from Greek Antiquity to the Nineteenth Century |date=2012 |publisher=OUP Oxford |isbn=978-0-19-162745-3 |language=en}}</ref> In 1857 [[Rudolf Clausius|Clausius]] developed a [[Kinetic theory of gases|gas-kinetic model]] which included the equation for [[mean free path]]. In the 1870s it was used to estimate gas molecule sizes, as well as an aforementioned comparison with [[visible light]] [[wavelength]] and an estimate from the thickness of [[soap bubble]] film at which its contractile force rapidly diminishes.<ref>{{Cite book |url=https://books.google.com/books?id=vnrkYGHPGmoC&pg=PA165 |title=The American chemist: a monthly journal of theoretical, analytical and technical chemistry |date=1877 |publisher=C. F. & W. H. Chandler |language=en}}</ref> By 1900, various estimates of mercury atom diameter averaged around 275±20 pm<ref name=":0" /> (modern estimates give 300±10 pm, see below).

In 1920, shortly after it had become possible to determine the sizes of atoms using [[X-ray crystallography]], it was suggested that all atoms of the same element have the same radii.<ref>
{{cite journal
 |last1=Bragg |first1=W. L.
 |year=1920
 |title=The arrangement of atoms in crystals
 |journal=[[Philosophical Magazine]]
 |volume=40|series=6|issue=236
 |pages=169–189
 |doi=10.1080/14786440808636111
|url=https://zenodo.org/record/1430834
 }}</ref>  However, in 1923, when more crystal data had become available, it was found that the approximation of an atom as a sphere does not necessarily hold when comparing the same atom in different crystal structures.<ref>
{{cite journal
 |last=Wyckoff |first=R. W. G.
 |year=1923
 |title=On the Hypothesis of Constant Atomic Radii
 |journal=[[Proceedings of the National Academy of Sciences of the United States of America]]
 |volume=9 |issue=2 |pages=33–38
 |bibcode = 1923PNAS....9...33W
 |doi=10.1073/pnas.9.2.33
 |pmid=16576657
 |pmc=1085234
|doi-access=free
 }}</ref>

==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.

==Empirically measured atomic radius==

The following table shows empirically measured '''covalent''' radii for the elements, as published by [[J. C. Slater]] in 1964.<ref name="slater64">
{{cite journal
 |last=Slater|first=J. C.
 |year=1964
 |title=Atomic Radii in Crystals
 |journal=[[Journal of Chemical Physics]]
 |volume=41 |issue=10 |pages=3199–3205
 |bibcode=1964JChPh..41.3199S
 |doi=10.1063/1.1725697
}}</ref> The values are in [[picometers]] (pm or 1×10<sup>&minus;12</sup>&nbsp;m), with an accuracy of about 5 pm. The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data.

{| wikitable width="80%" style="text-align:center"
| '''[[Periodic table group|Group]]'''<br><small>(column)</small>
| '''[[Alkali metal|1]]'''
| '''[[Alkaline earth metal|2]]'''
|
| '''[[Group 3 element|3]]'''
| '''[[Group 4 element|4]]'''
| '''[[Group 5 element|5]]'''
| '''[[Group 6 element|6]]'''
| '''[[Group 7 element|7]]'''
| '''[[Group 8 element|8]]'''
| '''[[Group 9 element|9]]'''
| '''[[Group 10 element|10]]'''
| '''[[Group 11 element|11]]'''
| '''[[Group 12 element|12]]'''
| '''[[Boron group|13]]'''
| '''[[Carbon group|14]]'''
| '''[[Pnictogen|15]]'''
| '''[[Chalcogen|16]]'''
| '''[[Halogen|17]]'''
| '''[[Noble gas|18]]'''
|-
| '''[[Periodic table period|Period]]'''<br><small>(row)</small>
|  colspan=21 |
|-
| '''[[Period 1 element|1]]'''
|  bgcolor="#ff1900" | [[Hydrogen|H]]<br/>25
|  colspan=17 |
|  bgcolor="#bbbbbb" | [[Helium|He]]<br/>&nbsp;<!--was 31-->
|-
| '''[[Period 2 element|2]]'''
|  bgcolor="#ff9100" | [[Lithium|Li]]<br/>145
|  bgcolor="#ff6900" | [[Beryllium|Be]]<br/>105
|  colspan=11 |
|  bgcolor="#ff5500" | [[Boron|B]]<br/>85
|  bgcolor="#ff4600" | [[Carbon|C]]<br/>70
|  bgcolor="#ff4100" | [[Nitrogen|N]]<br/>65
|  bgcolor="#ff3c00" | [[Oxygen|O]]<br/>60
|  bgcolor="#ff3200" | [[Fluorine|F]]<br/>50
|  bgcolor="#bbbbbb" | [[Neon|Ne]]<br/>&nbsp;<!--was 38-->
|-
| '''[[Period 3 element|3]]'''
|  bgcolor="#ffb400" | [[Sodium|Na]]<br/>180
|  bgcolor="#ff9600" | [[Magnesium|Mg]]<br/>150
|  colspan=11 |
|  bgcolor="#ff7d00" | [[Aluminium|Al]]<br/>125
|  bgcolor="#ff6e00" | [[Silicon|Si]]<br/>110
|  bgcolor="#ff6400" | [[Phosphorus|P]]<br/>100
|  bgcolor="#ff6400" | [[Sulfur|S]]<br/>100
|  bgcolor="#ff6400" | [[Chlorine|Cl]]<br/>100
|  bgcolor="#bbbbbb" | [[Argon|Ar]]<br/>&nbsp;<!--was 71-->
|-
| '''[[Period 4 element|4]]'''
|  bgcolor="#ffdc00" | [[Potassium|K]]<br/>220
|  bgcolor="#ffb400" | [[Calcium|Ca]]<br/>180
|
|  bgcolor="#ffa000" | [[Scandium|Sc]]<br/>160
|  bgcolor="#ff8c00" | [[Titanium|Ti]]<br/>140
|  bgcolor="#ff8700" | [[Vanadium|V]]<br/>135
|  bgcolor="#ff8c00" | [[Chromium|Cr]]<br/>140
|  bgcolor="#ff8c00" | [[Manganese|Mn]]<br/>140
|  bgcolor="#ff8c00" | [[Iron|Fe]]<br/>140
|  bgcolor="#ff8700" | [[Cobalt|Co]]<br/>135
|  bgcolor="#ff8700" | [[Nickel|Ni]]<br/>135
|  bgcolor="#ff8700" | [[Copper|Cu]]<br/>135
|  bgcolor="#ff8700" | [[Zinc|Zn]]<br/>135
|  bgcolor="#ff8700" | [[Gallium|Ga]]<br/>130
|  bgcolor="#ff7d00" | [[Germanium|Ge]]<br/>125
|  bgcolor="#ff7300" | [[Arsenic|As]]<br/>115
|  bgcolor="#ff7300" | [[Selenium|Se]]<br/>115
|  bgcolor="#ff7300" | [[Bromine|Br]]<br/>115
|  bgcolor="#bbbbbb" | [[Krypton|Kr]]<br/>&nbsp;
|-
| '''[[Period 5 element|5]]'''
|  bgcolor="#ffeb00" | [[Rubidium|Rb]]<br/>235
|  bgcolor="#ffc800" | [[Strontium|Sr]]<br/>200
|
|  bgcolor="#ffb400" | [[Yttrium|Y]]<br/>180
|  bgcolor="#ff9b00" | [[Zirconium|Zr]]<br/>155
|  bgcolor="#ff9100" | [[Niobium|Nb]]<br/>145
|  bgcolor="#ff9100" | [[Molybdenum|Mo]]<br/>145
|  bgcolor="#ff8700" | [[Technetium|Tc]]<br/>135
|  bgcolor="#ff8200" | [[Ruthenium|Ru]]<br/>130
|  bgcolor="#ff8700" | [[Rhodium|Rh]]<br/>135
|  bgcolor="#ff8c00" | [[Palladium|Pd]]<br/>140
|  bgcolor="#ffa000" | [[Silver|Ag]]<br/>160
|  bgcolor="#ff9b00" | [[Cadmium|Cd]]<br/>155
|  bgcolor="#ff9b00" | [[Indium|In]]<br/>155
|  bgcolor="#ff9100" | [[Tin|Sn]]<br/>145
|  bgcolor="#ff9100" | [[Antimony|Sb]]<br/>145
|  bgcolor="#ff8c00" | [[Tellurium|Te]]<br/>140
|  bgcolor="#ff8c00" | [[Iodine|I]]<br/>140
|  bgcolor="#bbbbbb" | [[Xenon|Xe]]<br/>&nbsp;
|-
| '''[[Period 6 element|6]]'''
|  bgcolor="#ffff00" | [[Caesium|Cs]]<br/>260
|  bgcolor="#ffd700" | [[Barium|Ba]]<br/>215
|  *<br/>&nbsp;
|  bgcolor="#ffaf00" | [[Lutetium|Lu]]<br/>175
|  bgcolor="#ff9b00" | [[Hafnium|Hf]]<br/>155
|  bgcolor="#ff9100" | [[Tantalum|Ta]]<br/>145
|  bgcolor="#ff8700" | [[Tungsten|W]]<br/>135
|  bgcolor="#ff8700" | [[Rhenium|Re]]<br/>135
|  bgcolor="#ff8200" | [[Osmium|Os]]<br/>130
|  bgcolor="#ff8700" | [[Iridium|Ir]]<br/>135
|  bgcolor="#ff8700" | [[Platinum|Pt]]<br/>135
|  bgcolor="#ff8700" | [[Gold|Au]]<br/>135
|  bgcolor="#ff9600" | [[Mercury (element)|Hg]]<br/>150
|  bgcolor="#ffbe00" | [[Thallium|Tl]]<br/>190
|  bgcolor="#ffb400" | [[Lead|Pb]]<br/>180
|  bgcolor="#ffa000" | [[Bismuth|Bi]]<br/>160
|  bgcolor="#ffbe00" | [[Polonium|Po]]<br/>190
|  bgcolor="#bbbbbb" | [[Astatine|At]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Radon|Rn]]<br/>&nbsp;
|-
| '''[[Period 7 element|7]]'''
|  bgcolor="#bbbbbb" | [[Francium|Fr]]<br/>&nbsp;
|  bgcolor="#ffd700" | [[Radium|Ra]]<br/>215
|  **<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Lawrencium|Lr]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Rutherfordium|Rf]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Dubnium|Db]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Seaborgium|Sg]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Bohrium|Bh]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Hassium|Hs]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Meitnerium|Mt]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Darmstadtium|Ds]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Roentgenium|Rg]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Copernicium|Cn]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Nihonium|Nh]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Flerovium|Fl]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Moscovium|Mc]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Livermorium|Lv]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Tennessine|Ts]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Oganesson|Og]]<br/>&nbsp;
|-
|
|-
|
|
|
|  *<br/>&nbsp;
|  bgcolor="#ffc300" | [[Lanthanum|La]]<br/>195
|  bgcolor="#ffb900" | [[Cerium|Ce]]<br/>185
|  bgcolor="#ffb900" | [[Praseodymium|Pr]]<br/>185
|  bgcolor="#ffb900" | [[Neodymium|Nd]]<br/>185
|  bgcolor="#ffb900" | [[Promethium|Pm]]<br/>185
|  bgcolor="#ffb900" | [[Samarium|Sm]]<br/>185
|  bgcolor="#ffb900" | [[Europium|Eu]]<br/>185
|  bgcolor="#ffb400" | [[Gadolinium|Gd]]<br/>180
|  bgcolor="#ffaf00" | [[Terbium|Tb]]<br/>175
|  bgcolor="#ffaf00" | [[Dysprosium|Dy]]<br/>175
|  bgcolor="#ffaf00" | [[Holmium|Ho]]<br/>175
|  bgcolor="#ffaf00" | [[Erbium|Er]]<br/>175
|  bgcolor="#ffaf00" | [[Thulium|Tm]]<br/>175
|  bgcolor="#ffaf00" | [[Ytterbium|Yb]]<br/>175
|-
|
|
|
|  **<br/>&nbsp;
|  bgcolor="#ffc300" | [[Actinium|Ac]]<br/>195
|  bgcolor="#ffb400" | [[Thorium|Th]]<br/>180
|  bgcolor="#ffb400" | [[Protactinium|Pa]]<br/>180
|  bgcolor="#ffaf00" | [[Uranium|U]]<br/>175
|  bgcolor="#ffaf00" | [[Neptunium|Np]]<br/>175
|  bgcolor="#ffaf00" | [[Plutonium|Pu]]<br/>175
|  bgcolor="#ffaf00" | [[Americium|Am]]<br/>175
|  bgcolor="#bbbbbb" | [[Curium|Cm]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Berkelium|Bk]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Californium|Cf]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Einsteinium|Es]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Fermium|Fm]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Mendelevium|Md]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Nobelium|No]]<br/>&nbsp;
|-
|  colspan=21 |
|}

==Explanation of the general trends==
[[File:Atomic number to radius graph.png|thumb|A graph comparing the atomic radius of elements with atomic numbers 1–100. Accuracy of ±5 pm.]]

Electrons in atoms fill [[electron shell]]s from the lowest available energy level. As a consequence of the [[Aufbau principle]], each new [[period (periodic table)|period]] begins with the first two elements filling the next unoccupied [[atomic orbital|s-orbital]]. Because an atom's s-orbital electrons are typically farthest from the nucleus, this results in a significant increase in atomic radius with the first elements of each period.

The atomic radius of each element generally decreases across each period due to an increasing number of protons, since an increase in the number of protons increases the attractive force acting on the atom's electrons. The greater attraction draws the electrons closer to the protons, decreasing the size of the atom. Down each group, the atomic radius of each element typically increases because there are more occupied 
electron [[electron shell|energy levels]] and therefore a greater distance between protons and electrons.

The increasing nuclear charge is partly counterbalanced by the increasing number of electrons—a phenomenon that is known as [[shielding effect|shielding]]—which explains why the size of atoms usually increases down each column despite an increase in attractive force from the nucleus. Electron shielding causes the attraction of an atom's nucleus on its electrons to decrease, so electrons occupying higher energy states farther from the nucleus experience reduced attractive force, increasing the size of the atom. However, elements in the 5d-block ([[lutetium]] to [[mercury (element)|mercury]]) are much smaller than this trend predicts due to the weak shielding of the 4f-subshell. This phenomenon is known as the [[lanthanide contraction]]. A similar phenomenon exists for [[actinoid contraction|actinides]]; however, the general instability of [[transuranic element]]s makes measurements for the remainder of the 5f-block difficult and for transactinides nearly impossible. Finally, for sufficiently heavy elements, the atomic radius may be decreased by [[relativistic quantum chemistry|relativistic effects]].<ref>{{cite journal |last1=Pitzer |first1=Kenneth S. |title=Relativistic effects on chemical properties |journal=Accounts of Chemical Research |date=1 August 1979 |volume=12 |issue=8 |pages=271–276 |doi=10.1021/ar50140a001|url=https://escholarship.org/uc/item/2vb947cs }}</ref> This is a consequence of electrons near the strongly charged nucleus traveling at a sufficient fraction of the speed of light to gain a nontrivial amount of mass.

The following table summarizes the main phenomena that influence the atomic radius of an element:

{| class="wikitable"
|-
! Factor !! Principle !! increase in...  !! ''tend to'' !! effect on radius
|-
| electron shells || quantum mechanics || principal and azimuthal [[quantum numbers]] || increase down each column || increases the atomic radius
|-
| nuclear charge || attractive force acting on electrons by protons in nucleus || atomic number || increase along each period (left to right) || decreases the atomic radius 
|-
| shielding || repulsive force acting on outermost shell electrons by inner electrons || number of electrons in inner shells || reduce the effect of nuclear charge || increases the atomic radius 
|}

===Lanthanide contraction===
{{main|Lanthanide contraction}}
The electrons in the 4f-[[Electron shell|subshell]], which is progressively filled from [[lanthanum]] (''[[Atomic number|Z]]''&nbsp;= 57) to [[ytterbium]] (''Z''&nbsp;= 70), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the [[lanthanide]]s have atomic radii which are smaller than would be expected and which are almost identical to the atomic radii of the elements immediately above them.<ref name="Jolly_contract">
{{cite book
 |last1=Jolly |first1=W. L.
 |year=1991
 |title=Modern Inorganic Chemistry
 |page=22 |edition=2nd
 |publisher=[[McGraw-Hill]]
 |isbn=978-0-07-112651-9
}}</ref> Hence [[lutetium]] is in fact slightly smaller than [[yttrium]], [[hafnium]] has virtually the same atomic radius (and chemistry) as [[zirconium]], and [[tantalum]] has an atomic radius similar to [[niobium]], and so forth.  The effect of the lanthanide contraction is noticeable up to [[platinum]] (''Z''&nbsp;= 78), after which it is masked by a [[relativistic effect]] known as the [[inert-pair effect]].{{Citation needed|date=February 2023}}

Due to lanthanide contraction, the 5 following observations can be drawn:

# The size of Ln<sup>3+</sup> ions regularly decreases with atomic number. According to [[Fajans' rules]], decrease in size of Ln<sup>3+</sup> ions increases the covalent character and decreases the basic character between Ln<sup>3+</sup> and  OH<sup>−</sup> ions in Ln(OH)<sub>3</sub>, to the point that Yb(OH)<sub>3</sub> and Lu(OH)<sub>3</sub> can dissolve with difficulty in hot concentrated NaOH. Hence the order of size of Ln<sup>3+</sup> is given: <br /> La<sup>3+</sup> > Ce<sup>3+</sup> > ..., ... > Lu<sup>3+</sup>.
# There is a regular decrease in their ionic radii.
# There is a regular decrease in their tendency to act as a reducing agent, with an increase in atomic number.
# The second and third rows of d-block transition elements are quite close in properties.
# Consequently, these elements occur together in natural minerals and are difficult to separate.

===d-block contraction===
{{main|d-block contraction}}
The d-block contraction is less pronounced than the lanthanide contraction but arises from a similar cause. In this case, it is the poor shielding capacity of the 3d-electrons which affects the atomic radii and chemistries of the elements immediately following the first row of the [[transition metal]]s, from [[gallium]] (''Z''&nbsp;= 31) to [[bromine]] (''Z''&nbsp;= 35).<ref name="Jolly_contract"/>

==Calculated atomic radius==
The following table shows atomic radii computed from theoretical models, as published by [[Enrico Clementi]] and others in 1967.<ref name="clem67">
{{cite journal
 |last1=Clementi |first1=E.
 |last2=Raimond |first2=D. L.
 |last3=Reinhardt |first3=W. P.
 |year=1967
 |title=Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons
 |journal=[[Journal of Chemical Physics]]
 |volume=47 |issue=4 |pages=1300–1307
 |bibcode = 1967JChPh..47.1300C
 |doi=10.1063/1.1712084
}}</ref> The values are in picometres (pm).

{| wikitable width="80%" style="text-align:center"
| '''[[Periodic table group|Group]]'''<br><small>(column)</small>
| '''[[Alkali metal|1]]'''
| '''[[Alkaline earth|2]]'''
|
| '''[[Group 3 element|3]]'''
| '''[[Group 4 element|4]]'''
| '''[[Group 5 element|5]]'''
| '''[[Group 6 element|6]]'''
| '''[[Group 7 element|7]]'''
| '''[[Group 8 element|8]]'''
| '''[[Group 9 element|9]]'''
| '''[[Group 10 element|10]]'''
| '''[[Coinage metal|11]]'''
| '''[[Group 12 element|12]]'''
| '''[[Boron group|13]]'''
| '''[[Carbon group|14]]'''
| '''[[Pnictogen|15]]'''
| '''[[Chalcogen|16]]'''
| '''[[Halogen|17]]'''
| '''[[Noble gas|18]]'''
|-
| '''[[Periodic table period|Period]]'''<br><small>(row)</small>
|  colspan=20 |
|-
| '''[[Period 1 element|1]]'''
|  bgcolor="#ff3500" | [[Hydrogen|H]]<br/>53
|  colspan=17 |
|  bgcolor="#ff1f00" | [[Helium|He]]<br/>31
|-
| '''[[Period 2 element|2]]'''
|  bgcolor="#ffa700" | [[Lithium|Li]]<br/>167
|  bgcolor="#ff7000" | [[Beryllium|Be]]<br/>112
|  colspan=11 |
|  bgcolor="#ff5700" | [[Boron|B]]<br/>87
|  bgcolor="#ff4300" | [[Carbon|C]]<br/>67
|  bgcolor="#ff3800" | [[Nitrogen|N]]<br/>56
|  bgcolor="#ff3000" | [[Oxygen|O]]<br/>48
|  bgcolor="#ff2a00" | [[Fluorine|F]]<br/>42
|  bgcolor="#ff2600" | [[Neon|Ne]]<br/>38
|-
| '''[[Period 3 element|3]]'''
|  bgcolor="#ffbe00" | [[Sodium|Na]]<br/>190
|  bgcolor="#ff9100" | [[Magnesium|Mg]]<br/>145
|  colspan=11 |
|  bgcolor="#ff7600" | [[Aluminium|Al]]<br/>118
|  bgcolor="#ff6f00" | [[Silicon|Si]]<br/>111
|  bgcolor="#ff6200" | [[Phosphorus|P]]<br/>98
|  bgcolor="#ff5800" | [[Sulfur|S]]<br/>88
|  bgcolor="#ff4f00" | [[Chlorine|Cl]]<br/>79
|  bgcolor="#ff4700" | [[Argon|Ar]]<br/>71
|-
| '''[[Period 4 element|4]]'''
|  bgcolor="#fff300" | [[Potassium|K]]<br/>243
|  bgcolor="#ffc200" | [[Calcium|Ca]]<br/>194
|
|  bgcolor="#ffb800" | [[Scandium|Sc]]<br/>184
|  bgcolor="#ffb000" | [[Titanium|Ti]]<br/>176
|  bgcolor="#ffab00" | [[Vanadium|V]]<br/>171
|  bgcolor="#ffa600" | [[Chromium|Cr]]<br/>166
|  bgcolor="#ffa100" | [[Manganese|Mn]]<br/>161
|  bgcolor="#ff9c00" | [[Iron|Fe]]<br/>156
|  bgcolor="#ff9800" | [[Cobalt|Co]]<br/>152
|  bgcolor="#ff9500" | [[Nickel|Ni]]<br/>149
|  bgcolor="#ff9100" | [[Copper|Cu]]<br/>145
|  bgcolor="#ff8e00" | [[Zinc|Zn]]<br/>142
|  bgcolor="#ff8800" | [[Gallium|Ga]]<br/>136
|  bgcolor="#ff7d00" | [[Germanium|Ge]]<br/>125
|  bgcolor="#ff7200" | [[Arsenic|As]]<br/>114
|  bgcolor="#ff6700" | [[Selenium|Se]]<br/>103
|  bgcolor="#ff5e00" | [[Bromine|Br]]<br/>94
|  bgcolor="#ff5800" | [[Krypton|Kr]]<br/>88
|-
| '''[[Period 5 element|5]]'''
|  bgcolor="#ffff0a" | [[Rubidium|Rb]]<br/>265
|  bgcolor="#ffdb00" | [[Strontium|Sr]]<br/>219
|
|  bgcolor="#ffd400" | [[Yttrium|Y]]<br/>212
|  bgcolor="#ffce00" | [[Zirconium|Zr]]<br/>206
|  bgcolor="#ffc600" | [[Niobium|Nb]]<br/>198
|  bgcolor="#ffbe00" | [[Molybdenum|Mo]]<br/>190
|  bgcolor="#ffb700" | [[Technetium|Tc]]<br/>183
|  bgcolor="#ffb600" | [[Ruthenium|Ru]]<br/>178
|  bgcolor="#ffac00" | [[Rhodium|Rh]]<br/>173
|  bgcolor="#ffa900" | [[Palladium|Pd]]<br/>169
|  bgcolor="#ffa500" | [[Silver|Ag]]<br/>165
|  bgcolor="#ffa100" | [[Cadmium|Cd]]<br/>161
|  bgcolor="#ff9c00" | [[Indium|In]]<br/>156
|  bgcolor="#ff9100" | [[Tin|Sn]]<br/>145
|  bgcolor="#ff8500" | [[Antimony|Sb]]<br/>133
|  bgcolor="#ff7b00" | [[Tellurium|Te]]<br/>123
|  bgcolor="#ff7300" | [[Iodine|I]]<br/>115
|  bgcolor="#ff6c00" | [[Xenon|Xe]]<br/>108
|-
| '''[[Period 6 element|6]]'''
|  bgcolor="#ffff2b" | [[Caesium|Cs]]<br/>298
|  bgcolor="#fffd00" | [[Barium|Ba]]<br/>253
|  *<br/>&nbsp;
|  bgcolor="#ffd900" | [[Lutetium|Lu]]<br/>217
|  bgcolor="#ffd000" | [[Hafnium|Hf]]<br/>208
|  bgcolor="#ffc800" | [[Tantalum|Ta]]<br/>200
|  bgcolor="#ffc100" | [[Tungsten|W]]<br/>193
|  bgcolor="#ffbc00" | [[Rhenium|Re]]<br/>188
|  bgcolor="#ffb900" | [[Osmium|Os]]<br/>185
|  bgcolor="#ffb400" | [[Iridium|Ir]]<br/>180
|  bgcolor="#ffb100" | [[Platinum|Pt]]<br/>177
|  bgcolor="#ffae00" | [[Gold|Au]]<br/>174
|  bgcolor="#ffab00" | [[Mercury (element)|Hg]]<br/>171
|  bgcolor="#ff9c00" | [[Thallium|Tl]]<br/>156
|  bgcolor="#ff9a00" | [[Lead|Pb]]<br/>154
|  bgcolor="#ff8f00" | [[Bismuth|Bi]]<br/>143
|  bgcolor="#ff8700" | [[Polonium|Po]]<br/>135
|  bgcolor="ff7f00" | [[Astatine|At]]<br/>127
|  bgcolor="#ff7800" | [[Radon|Rn]]<br/>120
|-  align=CENTER
| '''[[Period 7 element|7]]'''
|  bgcolor="#bbbbbb" | [[Francium|Fr]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Radium|Ra]]<br/>&nbsp;
|  **<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Lawrencium|Lr]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Rutherfordium|Rf]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Dubnium|Db]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Seaborgium|Sg]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Bohrium|Bh]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Hassium|Hs]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Meitnerium|Mt]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Darmstadtium|Ds]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Roentgenium|Rg]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Copernicium|Cn]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Nihonium|Nh]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Flerovium|Fl]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Moscovium|Mc]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Livermorium|Lv]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Tennessine|Ts]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Oganesson|Og]]<br/>&nbsp;
|-  align=CENTER
|
|-  align=CENTER
|
|
|
|  *<br/>&nbsp;
|  bgcolor="#ffe200" | [[Lanthanum|La]]<br/>226
|  bgcolor="#ffd200" | [[Cerium|Ce]]<br/>210
|  bgcolor="#fff700" | [[Praseodymium|Pr]]<br/>247
|  bgcolor="#ffce00" | [[Neodymium|Nd]]<br/>206
|  bgcolor="#ffcd00" | [[Promethium|Pm]]<br/>205
|  bgcolor="#ffee00" | [[Samarium|Sm]]<br/>238
|  bgcolor="#ffe700" | [[Europium|Eu]]<br/>231
|  bgcolor="#ffe900" | [[Gadolinium|Gd]]<br/>233
|  bgcolor="#ffe100" | [[Terbium|Tb]]<br/>225
|  bgcolor="#ffe400" | [[Dysprosium|Dy]]<br/>228
|  bgcolor="#ffe200" | [[Holmium|Ho]]<br/>226
|  bgcolor="#ffe200" | [[Erbium|Er]]<br/>226
|  bgcolor="#ffde00" | [[Thulium|Tm]]<br/>222
|  bgcolor="#ffde00" | [[Ytterbium|Yb]]<br/>222
|-
|
|
|
|  **<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Actinium|Ac]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Thorium|Th]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Protactinium|Pa]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Uranium|U]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Neptunium|Np]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Plutonium|Pu]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Americium|Am]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Curium|Cm]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Berkelium|Bk]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Californium|Cf]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Einsteinium|Es]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Fermium|Fm]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Mendelevium|Md]]<br/>&nbsp;
|  bgcolor="#bbbbbb" | [[Nobelium|No]]<br/>&nbsp;
|}

==See also==
*[[Atomic radii of the elements (data page)]]
*[[Chemical bond]]
*[[Covalent radius]]
*[[Bond length]]
*[[Steric hindrance]]
*[[Kinetic diameter]]

==References==
{{reflist|30em}}

{{DEFAULTSORT:Atomic Radius}}
[[Category:Atomic radius]]
[[Category:Properties of chemical elements]]