Periodic Trends — Atomic and Ionic Radii

Atomic radii reported in units of picometers (pm).

Data taken from John Emsley, The Elements, 3rd edition.  Oxford:  Clarendon Press, 1998.

 

The atomic radius is the distance from the nucleus of an atom to the outermost electrons.  Since the orbitals around an atom are defined in terms of a probability distribution in quantum mechanics, and do not have fixed boundaries, determining where an atom "stops" is not very straightforward.  By comparing the bond lengths of a number of representative compounds of an element, an average size for most atoms can be determined.

The atomic radius can also be defined in other ways.  The van der Waals radius (also known as the nonbonding atomic radius) is the radius of an atom which is not bonded to other atoms; this is determined by measuring the distance between atomic nuclei which are in direct but nonbonding contact with each other in a crystal lattice.  The covalent atomic radius (also known as the bonding atomic radius) is determined for metals by taking one-half of the distance between two adjacent atoms in a metallic crystal, or one-half the distance between like bonded atoms for nonmetals.

Unfortunately, it is not possible to determine the radius for every element on the periodic table in the same way, and consequently, it is sometimes difficult to make comparisons between different sets of data.  In the table above, most of the atomic radii listed are average atomic radii, while for the halogens (Group 7A) and the noble gases (Group 8A) the covalent radius is used.

Atomic radii vary in a predictable way across the periodic table.  As can be seen in the figures below, the atomic radius increases from top to bottom in a group, and decreases from left to right across a period.  Thus, helium is the smallest element, and francium is the largest.

• From top to bottom in a group, orbitals corresponding to higher values of the principal quantum number (n) are being added, which are on average further away from the nucleus, thus causing the size of the atom to increase.
• From left to right across a period, more protons are being added to the nucleus, but the electrons which are being added are being added to the valence shell, not to the lower energy levels.  As more protons are added to the nucleus, the electrons in the valence shell feel a higher effective nuclear charge — the sum of the charges on the protons in the nucleus and the charges on the inner, core electrons.  (See figure below.)  The valence electrons are therefore held more tightly, and the size of the atom contracts across a period.

 

The following charts illustrate the general trends in the radii of atoms:

 

The sizes of cations and anions follow similar trends to those of neutral atoms.  In general, anions are larger than the corresponding neutral atom, since adding electrons increases the number of electron-electron repulsion interactions that take place.  Cations are smaller than the corresponding neutral atoms, since the valence electrons, which are furthest away from the nucleus, are lost.  Taking more electrons away from the cation further reduces the radius of the ion.

The table below illustrates these trends for the main group elements.  For elements which form more than one cation, the cation charges and sizes are listed in two separate columns.  The transition metals and inner transition metals have been omitted, since almost all of those elements can form two or more possible cations.

 

Sizes of Common Cations and Anions of the Main Group Elements

Atomic Number	Name	Neutral  Atom (ppm)	Cation1 Charge	Cation1 Radius (ppm)	Cation2 Charge	Cation2 Radius (ppm)	Anion Charge	Anion Radius (ppm)
1	Hydrogen	78	1+	0.00066			1-	154
2	Helium	32
3	Lithium	152	1+	78
4	Beryllium	113	2+	34
5	Boron	83	3+	23
6	Carbon	77					4-	260
7	Nitrogen	71					3-	171
8	Oxygen	73					2-	132
9	Fluorine	71					1-	133
10	Neon	70
11	Sodium	186	1+	98
12	Magnesium	160	2+	79
13	Aluminum	143	3+	57
14	Silicon	117	4+	26			4-	271
15	Phosphorus	115					3-	212
16	Sulfur	104					2-	184
17	Chlorine	99					1-	181
18	Argon	98
19	Potassium	227	1+	133
20	Calcium	197	2+	106
31	Gallium	122	3+	62	1+	113
32	Germanium	123	2+	90			4-	272
33	Arsenic	125	5+	46	3+	69	3-	222
34	Selenium	117	4+	69			2-	191
35	Bromine	114					1-	195
36	Krypton	112
37	Rubidium	248	1+	149
38	Strontium	215	2+	127
49	Indium	163	3+	92	1+	132
50	Tin	141	4+	74	2+	93	4-	294
51	Antimony	141	5+	62	3+	89	3-	245
52	Tellurium	143	6+	56	4+	97	2-	211
53	Iodine	133					1-	196
54	Xenon	130
55	Cesium	265	1+	165
56	Barium	217	2+	143
81	Thallium	170	3+	105	1+	149
82	Lead	175	4+	84	2+	132
83	Bismuth	155	5+	74	3+	96
84	Polonium	167	4+	65			2-	230
85	Astatine		5+	57			1-	227
86	Radon	145
87	Francium	270	1+	180
88	Radium	223	2+	152

Data taken from John Emsley, The Elements, 3rd edition.  Oxford:  Clarendon Press, 1998.