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 radii up to zinc (30)

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

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".[2] 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
(a) These radii are taken from M. Mantina, A.C. Chamberlin, R. Valero, C.J. Cramer, and D.G. Truhlar, J. Phys. Chem. 2009, 113, 5806.
(b) 12 coordinate
(c) gallium has an anomalous crystal structure
(d) 10 coordinate
(e) uranium, neptunium and plutonium have irregular structures

References

Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). Wiley. p. 1385. ISBN 978-0-471-84997-1.
https://www.merriam-webster.com/dictionary/empirical

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

Atomic radius (empirical)

J.C. Slater (1964). "Atomic Radii in Crystals". J. Chem. Phys. 41 (10): 3199–3204. Bibcode:1964JChPh..41.3199S. doi:10.1063/1.1725697.

Atomic radius (calculated)

E. Clementi; D.L.Raimondi; W.P. Reinhardt (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". J. Chem. Phys. 47 (4): 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.

Van der Waals radius

A. Bondi (1964). "van der Waals Volumes and Radii". J. Phys. Chem. 68 (3): 441–451. doi:10.1021/j100785a001.
M. Mantina; A.C. Chamberlin; R. Valero; C.J. Cramer; D.G. Truhlar (2009). "Consistent van der Waals Radii for the Whole Main Group". J. Phys. Chem. A. 113 (19): 5806–12. Bibcode:2009JPCA..113.5806M. doi:10.1021/jp8111556. PMC 3658832. PMID 19382751.

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.

Triple-bond covalent radii

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. Mean-square deviation 3pm.
Triple-Bond Covalent Radii Table online

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.

[2] ttps://www.merriam-webster.com/dictionary/empirical