The atomic radius of a chemical element is a measure of the size of its atoms, usually
the mean or typical distance from the centre of the nucleus to the boundary of the surrounding
cloud of electrons. Since the boundary is not a well-defined physical entity, there
are various non-equivalent definitions of atomic radius. Three widely used definitions
of atomic radius are Van der Waals radius, ionic radius, and covalent 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. Electrons do not have definite orbits, or
sharply defined ranges. Rather, their positions must be described as probability distributions
that taper off gradually as one moves away from the nucleus, without a sharp cutoff.
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 pm, or between 0.3 and 3 angstroms. Therefore,
the radius of an atom is more than 10,000 times the radius of its nucleus, and less
than 1/1000 of the wavelength of visible light.
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 crystals, and the size and shape of molecules.
Atomic radii vary in a predictable and explicable manner across the periodic table. For instance,
the radii generally decrease along each period of the table, from the alkali metals to the
noble gases; and increase down each group. 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 can be explained by the electron shell theory of the atom;
they provided important evidence for the development and confirmation of quantum theory. The atomic
radii decreases across the Periodic Table because as the atomic number increases, the
number of protons increases across the period, but the extra electrons are only added to
the same quantum shell. Therefore, the effective nuclear charge towards the outermost electrons
increases, drawing the outermost electrons closer. As a result, the electron cloud contracts
and the atomic radii decreases.
History 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. 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.
Definitions Widely used definitions of atomic radius include:
Van der Waals radius: in principle, half the minimum distance between the nuclei of two
atoms of the element that are not bound to the same molecule.
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 should equal the sum
of their ionic radii. Covalent radius: the nominal radius of the
atoms of an element when 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 should equal the sum of their covalent radii.
Metallic radius: the nominal radius of atoms of an element when joined to other atoms by
metallic bonds. Bohr radius: the radius of the lowest-energy
electron orbit predicted by Bohr model of the atom. It is only applicable to 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. Empirically measured atomic radii
The following table shows empirically measured covalent radii for the elements, as published
by J. C. Slater in 1964. The values are in picometers, 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. Explanation of the general trends
The way the atomic radius varies with increasing atomic number can be explained by the arrangement
of electrons in shells of fixed capacity. The shells are generally filled in order of
increasing radius, since the negatively charged electrons are attracted by the positively
charged protons in the nucleus. As the atomic number increases along each row of the periodic
table, the additional electrons go into the same outermost shell; whose radius gradually
contracts, due to the increasing nuclear charge. In a noble gas, the outermost shell is completely
filled; therefore, the additional electron of next alkali metal will go into the next
outer shell, accounting for the sudden increase in the atomic radius.
The increasing nuclear charge is partly counterbalanced by the increasing number of electrons, a phenomenon
that is known as shielding; which explains why the size of atoms usually increases down
each column. However, there is one notable exception, known as the lanthanide contraction:
the 5d block of elements are much smaller than one would expect, due to the shielding
caused by the 4f electrons. The following table summarizes the main phenomena
that influence the atomic radius of an element: Lanthanide contraction
The electrons in the 4f-subshell, which is progressively filled from cerium to lutetium,
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 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, after which it is masked by a relativistic
effect known as the inert pair effect. Due to lanthanide contraction, the 5 following
observations can be drawn: The size of Ln3+ ions regularly decreases
with atomic number. According to Fajans' rules, decrease in size of Ln3+ ions increases the
covalent character and decreases the basic character between Ln3+ and OH− ions in Ln(OH)3.
Hence the order of size of Ln3+ is given: La3+ > Ce3+ > ..., ... > Lu3+.
There is a regular decrease in their ionic radii.
There is a regular decrease in their tendency to act as a reducing agent, with 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
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 to bromine.
Calculated atomic radii The following table shows atomic radii computed
from theoretical models, as published by Enrico Clementi and others in 1967. The values are
in picometres. See also
Atomic radii of the elements Chemical bond
Covalent radius Bond length
Steric hindrance References