Atomic radii of the elements (data page)

The atomic radius of a chemical element is the distance from the center of the nucleus to the outermost shell of an electron. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Depending on the definition, the term may apply only to isolated atoms, or also to atoms in condensed matter, covalently bound in molecules, or in ionized and excited states; and its value may be obtained through experimental measurements, or computed from theoretical models. Under some definitions, the value of the radius may depend on the atom's state and context.[1]

Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease rightward along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group (column). The radius increases sharply between the noble gas at the end of each period and the alkali metal at the beginning of the next period. These trends of the atomic radii (and of various other chemical and physical properties of the elements) can be explained by the electron shell theory of the atom; they provided important evidence for the development and confirmation of quantum theory.

Atomic radius

Note: All measurements given are in picometers (pm). For more recent data on covalent radii see Covalent radius. Just as atomic units are given in terms of the atomic mass unit (approximately the proton mass), the physically appropriate unit of length here is the Bohr radius, which is the radius of a hydrogen atom. The Bohr radius is consequently known as the "atomic unit of length". It is often denoted by a₀ and is approximately 53 pm. Hence, the values of atomic radii given here in picometers can be converted to atomic units by dividing by 53, to the level of accuracy of the data given in this table.

atomic number	symbol	name	empirical †	Calculated	van der Waals	Covalent (single bond)	Covalent (triple bond)	Metallic
1	H	hydrogen	25[2]	53	120[3] or 110[4]	32
2	He	helium	120	31[5]	140[3][4]	46
3	Li	lithium	145[2]	167[5]	182[3] or 181[4]	133		152
4	Be	beryllium	105[2]	112[5]	153[4]	102	85[6]	112
5	B	boron	85[2]	87[5]	192[4]	85	73[6]
6	C	carbon	70[2]	67[5]	170[3][4]	75	60[6]
7	N	nitrogen	65[2]	56[5]	155[3][4]	71	54[6]
8	O	oxygen	60[2]	48[5]	152[3][4]	63	53[6]
9	F	fluorine	50[2]	42[5]	147[3][4]	64	53[6]
10	Ne	neon	160[7]	38[5]	154[3][4]	67
11	Na	sodium	180[2]	190[5]	227[3][4]	155		186
12	Mg	magnesium	150[2]	145[5]	173[3][4]	139	127[6]	160
13	Al	aluminium	125[2]	118[5]	184[4]	126	111[6]	143
14	Si	silicon	110[2]	111[5]	210[3][4]	116	102[6]
15	P	phosphorus	100[2]	98[5]	180[3][4]	111	94[6]
16	S	sulfur	100[2]	88[5]	180[3][4]	103	95[6]
17	Cl	chlorine	100[2]	79[5]	175[3][4]	99	93[6]
18	Ar	argon	71	71[5]	188[3][4]	96	96[6]
19	K	potassium	220[2]	243[5]	275[3][4]	196		227
20	Ca	calcium	180[2]	194[5]	231[4]	171	133[6]	197
21	Sc	scandium	160[2]	184[5]	211	148	114[6]	162 ^b
22	Ti	titanium	140[2]	176[5]		136	108[6]	147
23	V	vanadium	135[2]	171[5]		134	106[6]	134 ^b
24	Cr	chromium	140[2]	166[5]		122	103[6]	128 ^b
25	Mn	manganese	140[2]	161[5]		119	103[6]	127 ^b
26	Fe	iron	140[2]	156[5]		116	102[6]	126 ^b
27	Co	cobalt	135[2]	152[5]		111	96[6]	125 ^b
28	Ni	nickel	135[2]	149[5]	163[3]	110	101[6]	124 ^b
29	Cu	copper	135[2]	145[5]	140[3]	112	120[6]	128 ^b
30	Zn	zinc	135[2]	142[5]	139[3]	118		134 ^b
31	Ga	gallium	130[2]	136[5]	187[3][4]	124	121[6]	135 ^c
32	Ge	germanium	125[2]	125[5]	211[4]	121	114[6]
33	As	arsenic	115[2]	114[5]	185[3][4]	121	106[6]
34	Se	selenium	115[2]	103[5]	190[3][4]	116	107[6]
35	Br	bromine	115[2]	94[5]	185[3] or 183[4]	114	110[6]
36	Kr	krypton		88[5]	202[3][4]	117	108[6]
37	Rb	rubidium	235[2]	265[5]	303[4]	210		248
38	Sr	strontium	200[2]	219[5]	249[4]	185	139[6]	215
39	Y	yttrium	180[2]	212[5]		163	124[6]	180 ^b
40	Zr	zirconium	155[2]	206[5]		154	121[6]	160
41	Nb	niobium	145[2]	198[5]		147	116[6]	146 ^b
42	Mo	molybdenum	145[2]	190[5]		138	113[6]	139 ^b
43	Tc	technetium	135[2]	183[5]		128	110[6]	136 ^b
44	Ru	ruthenium	130[2]	178[5]		125	103[6]	134 ^b
45	Rh	rhodium	135[2]	173[5]		125	106[6]	134 ^b
46	Pd	palladium	140[2]	169[5]	163[3]	120	112[6]	137 ^b
47	Ag	silver	160[2]	165[5]	172[3]	128	137[6]	144 ^b
48	Cd	cadmium	155[2]	161[5]	158[3]	136		151 ^b
49	In	indium	155[2]	156[5]	193[3][4]	142	146[6]	167
50	Sn	tin	145[2]	145[5]	217[3][4]	140	132[6]
51	Sb	antimony	145[2]	133[5]	206[4]	140	127[6]
52	Te	tellurium	140[2]	123[5]	206[3][4]	136	121[6]
53	I	iodine	140[2]	115[5]	198[3][4]	133	125[6]
54	Xe	xenon		108[5]	216[3][4]	131	122[6]
55	Cs	caesium	260[2]	298[5]	343[4]	232		265
56	Ba	barium	215[2]	253[5]	268[4]	196	149[6]	222
57	La	lanthanum	195[2]	226		180	139[6]	187 ^b
58	Ce	cerium	185[2]	210		163	131[6]	181.8 ^c
59	Pr	praseodymium	185[2]	247[5]		176	128[6]	182.4 ^c
60	Nd	neodymium	185[2]	206[5]		174		181.4 ^c
61	Pm	promethium	185[2]	205[5]		173		183.4 ^c
62	Sm	samarium	185[2]	238[5]		172		180.4 ^c
63	Eu	europium	185[2]	231[5]		168		180.4 ^c
64	Gd	gadolinium	180[2]	233[5]		169	132[6]	180.4 ^c
65	Tb	terbium	175[2]	225[5]		168		177.3 ^c
66	Dy	dysprosium	175[2]	228[5]		167		178.1 ^c
67	Ho	holmium	175[2]	226[5]		166		176.2 ^c
68	Er	erbium	175[2]	226[5]		165		176.1 ^c
69	Tm	thulium	175[2]	222[5]		164		175.9 ^c
70	Yb	ytterbium	175[2]	222[5]		170		176 ^c
71	Lu	lutetium	175[2]	217[5]		162	131[6]	173.8 ^c
72	Hf	hafnium	155[2]	208[5]		152	122[6]	159
73	Ta	tantalum	145[2]	200[5]		146	119[6]	146 ^b
74	W	tungsten	135[2]	193[5]		137	115[6]	139 ^b
75	Re	rhenium	135[2]	188[5]		131	110[6]	137 ^b
76	Os	osmium	130[2]	185[5]		129	109[6]	135 ^b
77	Ir	iridium	135[2]	180[5]		122	107[6]	135.5 ^b
78	Pt	platinum	135[2]	177[5]	175[3]	123	110[6]	138.5 ^b
79	Au	gold	135[2]	174[5]	166[3]	124	123[6]	144 ^b
80	Hg	mercury	150[2]	171[5]	155[3]	133		151 ^b
81	Tl	thallium	190[2]	156[5]	196[3][4]	144	150[6]	170
82	Pb	lead	180	154[5]	202[3][4]	144	137[6]
83	Bi	bismuth	160[2]	143[5]	207[4]	151	135[6]
84	Po	polonium	190[2]	135[5]	197[4]	145	129[6]
85	At	astatine		127[5]	202[4]	147	138[6]
86	Rn	radon		120[5]	220[4]	142	133[6]
87	Fr	francium			348[4]
88	Ra	radium	215[2]		283[4]	201	159[6]
89	Ac	actinium	195[2]			186	140[6]
90	Th	thorium	180[2]			175	136[6]	179 ^b
91	Pa	protactinium	180[2]			169	129[6]	163 ^d
92	U	uranium	175[2]		186[3]	170	118[6]	156 ^e
93	Np	neptunium	175[2]			171	116[6]	155 ^e
94	Pu	plutonium	175[2]			172		159 ^e
95	Am	americium	175[2]			166		173 ^b
96	Cm	curium	176			166		174 ^b
97	Bk	berkelium						170 ^b
98	Cf	californium						186±2 ^b
99	Es	einsteinium						186±2 ^b
100	Fm	fermium
101	Md	mendelevium
102	No	nobelium
103	Lr	lawrencium
104	Rf	rutherfordium					131[6]
105	Db	dubnium					126[6]
106	Sg	seaborgium					121[6]
107	Bh	bohrium					119[6]
108	Hs	hassium					118[6]
109	Mt	meitnerium					113[6]
110	Ds	darmstadtium					112[6]
111	Rg	roentgenium					118[6]
112	Cn	copernicium					130[6]
113	Nh	nihonium
114	Fl	flerovium
115	Mc	moscovium
116	Lv	livermorium
117	Ts	tennessine
118	Og	oganesson

Notes

Difference between empirical and experimental data: Empirical data basically means, "originating in or based on observation or experience" or "relying on experience or observation alone often without due regard for system and theory data".[8] It basically means that you measured it through physical observation, and a lot of experiments generating the same results. Although, note that the values are not calculated by a formula. However, often the empirical results then become an equation of estimation. Experimental data on the other hand are only based on theories. Such theoretical predictions are useful when there are no ways of measuring radii experimentally, if you want to predict the radius of an element that hasn't been discovered yet, or it has too short of a half-life.
The radius of an atom is not a uniquely defined property and depends on the definition. Data derived from other sources with different assumptions cannot be compared.
† to an accuracy of about 5 pm
(b) 12 coordinate
(c) gallium has an anomalous crystal structure
(d) 10 coordinate
(e) uranium, neptunium and plutonium have irregular structures
Triple bond mean-square deviation 3pm.

References

Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). Wiley. p. 1385. ISBN 978-0-471-84997-1.
J.C. Slater (1964). "Atomic Radii in Crystals". The Journal of Chemical Physics. 41 (10): 3199–3204. Bibcode:1964JChPh..41.3199S. doi:10.1063/1.1725697.
A. Bondi (1964). "van der Waals Volumes and Radii". The Journal of Physical Chemistry. 68 (3): 441–451. doi:10.1021/j100785a001.
Mantina, Manjeera; Chamberlin, Adam C.; Valero, Rosendo; Cramer, Christopher J.; Truhlar, Donald G. (2009-04-21). "Consistent van der Waals Radii for the Whole Main Group". The Journal of Physical Chemistry A. 113 (19). American Chemical Society (ACS): 5806–5812. Bibcode:2009JPCA..113.5806M. doi:10.1021/jp8111556. ISSN 1089-5639. PMC 3658832. PMID 19382751.
E. Clementi; D.L.Raimondi; W.P. Reinhardt (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". The Journal of Chemical Physics. 47 (4): 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.
S. Riedel; P.Pyykkö, M. Patzschke; Patzschke, M (2005). "Triple-Bond Covalent Radii". Chem. Eur. J. 11 (12): 3511–3520. doi:10.1002/chem.200401299. PMID 15832398.
Neon has van der Waal's radii thus its radii is the highest in its period
"Empirical Definition & Meaning - Merriam-Webster".

Data is as quoted at http://www.webelements.com/ from these sources:

Covalent radii (single bond)

R.T. Sanderson (1962). Chemical Periodicity. New York, USA: Reinhold.
L.E. Sutton, ed. (1965). "Supplement 1956–1959, Special publication No. 18". Table of interatomic distances and configuration in molecules and ions. London, UK: Chemical Society.
J.E. Huheey; E.A. Keiter & R.L. Keiter (1993). Inorganic Chemistry : Principles of Structure and Reactivity (4th ed.). New York, USA: HarperCollins. ISBN 0-06-042995-X.
W.W. Porterfield (1984). Inorganic chemistry, a unified approach. Reading Massachusetts, USA: Addison Wesley Publishing Co. ISBN 0-201-05660-7.
A.M. James & M.P. Lord (1992). Macmillan's Chemical and Physical Data. MacMillan. ISBN 0-333-51167-0.

Metallic radius

Greenwood, Norman N.; Earnshaw, Alan (1997). Chemistry of the Elements (2nd ed.). Butterworth-Heinemann. ISBN 978-0-08-037941-8.

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[1] Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). Wiley. p. 1385. ISBN 978-0-471-84997-1.

[Slater1964-2] J.C. Slater (1964). "Atomic Radii in Crystals". The Journal of Chemical Physics. 41 (10): 3199–3204. Bibcode:1964JChPh..41.3199S. doi:10.1063/1.1725697.

[Bondi1964-3] A. Bondi (1964). "van der Waals Volumes and Radii". The Journal of Physical Chemistry. 68 (3): 441–451. doi:10.1021/j100785a001.

[Mantina2009-4] Mantina, Manjeera; Chamberlin, Adam C.; Valero, Rosendo; Cramer, Christopher J.; Truhlar, Donald G. (2009-04-21). "Consistent van der Waals Radii for the Whole Main Group". The Journal of Physical Chemistry A. 113 (19). American Chemical Society (ACS): 5806–5812. Bibcode:2009JPCA..113.5806M. doi:10.1021/jp8111556. ISSN 1089-5639. PMC 3658832. PMID 19382751.

[Clementi1967-5] E. Clementi; D.L.Raimondi; W.P. Reinhardt (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". The Journal of Chemical Physics. 47 (4): 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.

[Pyykkö-6] S. Riedel; P.Pyykkö, M. Patzschke; Patzschke, M (2005). "Triple-Bond Covalent Radii". Chem. Eur. J. 11 (12): 3511–3520. doi:10.1002/chem.200401299. PMID 15832398.

[7] Neon has van der Waal's radii thus its radii is the highest in its period

[8] "Empirical Definition & Meaning - Merriam-Webster".