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Atomic radius

Atomic radius

Atomic radius, and more generally the size of an atom, is not a precisely defined physical quantity, nor is it constant in all circumstances. The value assigned to the radius of a particular atom always depends on the definition chosen for "atomic radius," and the appropriate definition depends on the context.

The term "atomic radius" itself is problematic: it may be restricted to the size of free atoms, or it may be used as a general term for the different measures of the size of atoms, both bound in molecules and free. In the latter case, which is the approach adopted here, it should also include ionic radius, as the distinction between covalent and ionic bonding is itself somewhat arbitrary.

The atomic radius is determined entirely by the electrons: The size of the atomic nucleus is measured in femtometres, 100,000 times smaller than the cloud of electrons. Electrons, however, do not have definite positions—although they are more likely to be in certain regions than others—and the electron cloud does not have sharp edges.

Despite (or maybe because of) these difficulties, many different attempts have been made to quantify the size of atoms (and ions), based both on experimental measurements and calculation methods. It is undeniable that atoms do behave as if they were spheres with a radius of 30–300 pm, that atomic size varies in a predictable and explicable manner across the periodic table and that this variation has important consequences for the chemistry of the elements.

Periodic trends in atomic radius

Atomic radius tends to increase as one proceeds down any group of the periodic table. This trend is intuitively satisfying: atoms with more electrons have larger radii. As one proceeds across any row of the periodic table, a more complex rationale is required: atoms contract in size within a period from left to right. This contraction results from the increasing number of protons in the nucleus. Protons make little contribution to the size of the atom, but they increase the positive charge of the nucleus, which draws the electrons into tighter orbitals.

factor principle increase with... tend to effect
electron shells quantum mechanics Principal Quantum Number, Azimuthal Quantum Number atomic radius↑ increase on descending a group
nuclear charge attractive force acting on electrons by protons in nucleus atomic number atomic radius↓ decrease on passing along a period
shielding repulsive force acting on outermost shell electrons by inner electrons number of electron shells atomic radius↑ reduce the effect of the 2nd factor

The increasing nuclear charge is partly counterbalanced by the increasing number of electrons in a phenomenon that is known as shielding, which is why the size of atoms usually increases as a group is descended. However, there are two occasions where shielding is less effective: in these cases, the atoms are smaller than would otherwise be expected.

Lanthanide contraction

The electrons in the 4f-subshell, which is progressively filled from cerium (Z = 58) to lutetium (Z = 71), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the lanthanides 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. Hence 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 = 78), after which it is masked by a relativistic effect known as the inert pair effect.

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 metals, from gallium (Z = 31) to bromine (Z = 35).

Empirically measured atomic radius

Empirically measured atomic radius in picometres (pm) to an accuracy of about 5 pm

Group (vertical) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period (horizontal)
1 H
25
He
 
2 Li
145
Be
105
B
85
C
70
N
65
O
60
F
50
Ne
 
3 Na
180
Mg
150
Al
125
Si
110
P
100
S
100
Cl
100
Ar
71
4 K
220
Ca
180
Sc
160
Ti
140
V
135
Cr
140
Mn
140
Fe
140
Co
135
Ni
135
Cu
135
Zn
135
Ga
130
Ge
125
As
115
Se
115
Br
115
Kr
 
5 Rb
235
Sr
200
Y
180
Zr
155
Nb
145
Mo
145
Tc
135
Ru
130
Rh
135
Pd
140
Ag
160
Cd
155
In
155
Sn
145
Sb
145
Te
140
I
140
Xe
 
6 Cs
260
Ba
215
*
 
Hf
155
Ta
145
W
135
Re
135
Os
130
Ir
135
Pt
135
Au
135
Hg
150
Tl
190
Pb
180
Bi
160
Po
190
At
 
Rn
 
7 Fr
 
Ra
215
**
 
Rf
 
Db
 
Sg
 
Bh
 
Hs
 
Mt
 
Ds
 
Rg
 
Uub
 
Uut
 
Uuq
 
Uup
 
Uuh
 
Uus
 
Uuo
 
Lanthanides *
 
La
195
Ce
185
Pr
185
Nd
185
Pm
185
Sm
185
Eu
185
Gd
180
Tb
175
Dy
175
Ho
175
Er
175
Tm
175
Yb
175
Lu
175
Actinides **
 
Ac
195
Th
180
Pa
180
U
175
Np
175
Pu
175
Am
175
Cm
 
Bk
 
Cf
 
Es
 
Fm
 
Md
 
No
 
Lr
 
Periodic table of empirically measured atomic radius in picometres (pm) to an accuracy of about 5 pm

See also Periodic table

Reference: J.C. Slater, J. Chem. Phys. 1964, 41, 3199.

Calculated atomic radius

Calculated atomic radius in picometres (pm)

Group (vertical) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period (horizontal)
1 H
53
He
31
2 Li
167
Be
112
B
87
C
67
N
56
O
48
F
42
Ne
38
3 Na
190
Mg
145
Al
118
Si
111
P
98
S
88
Cl
79
Ar
71
4 K
243
Ca
194
Sc
184
Ti
176
V
171
Cr
166
Mn
161
Fe
156
Co
152
Ni
149
Cu
145
Zn
142
Ga
136
Ge
125
As
114
Se
103
Br
94
Kr
88
5 Rb
265
Sr
219
Y
212
Zr
206
Nb
198
Mo
190
Tc
183
Ru
178
Rh
173
Pd
169
Ag
165
Cd
161
In
156
Sn
145
Sb
133
Te
123
I
115
Xe
108
6 Cs
298
Ba
253
*
 
Hf
208
Ta
200
W
193
Re
188
Os
185
Ir
180
Pt
177
Au
174
Hg
171
Tl
156
Pb
154
Bi
143
Po
135
At
 
Rn
120
7 Fr
 
Ra
 
**
 
Rf
 
Db
 
Sg
 
Bh
 
Hs
 
Mt
 
Ds
 
Rg
 
Uub
 
Uut
 
Uuq
 
Uup
 
Uuh
 
Uus
 
Uuo
 
Lanthanides *
 
La
 
Ce
 
Pr
247
Nd
206
Pm
205
Sm
238
Eu
231
Gd
233
Tb
225
Dy
228
Ho
 
Er
226
Tm
222
Yb
222
Lu
217
Actinides **
 
Ac
 
Th
 
Pa
 
U
 
Np
 
Pu
 
Am
 
Cm
 
Bk
 
Cf
 
Es
 
Fm
 
Md
 
No
 
Lr
 
Periodic table of calculated atomic radius in picometres (pm)

See also Periodic table

Reference: E. Clementi, D.L.Raimondi, and W.P. Reinhardt, J. Chem. Phys. 1967, 47, 1300.

See also

References

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