HOME

TheInfoList



OR:

The atomic radius of a
chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
is a measure of the size of its
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, a ...
, usually the mean or typical distance from the center of the
nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: * Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucl ...
to the outermost isolated
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
. Since the boundary is not a well-defined physical entity, there are various non-equivalent definitions of atomic radius. Four widely used definitions of atomic radius are: Van der Waals radius, ionic radius, metallic radius and covalent radius. Typically, because of the difficulty to isolate atoms in order to measure their radii separately, atomic radius is measured in a chemically bonded state; however theoretical calculations are simpler when considering atoms in isolation. The dependencies on environment, probe, and state lead to a multiplicity of definitions. Depending on the definition, the term may apply to atoms in condensed matter, covalently bonding in
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s, or in ionized and
excited state In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any quantum state of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). Excitation refers to ...
s; and its value may be obtained through experimental measurements, or computed from theoretical models. The value of the radius may depend on the atom's state and context. Electrons do not have definite orbits nor sharply defined ranges. Rather, their positions must be described as
probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon ...
s that taper off gradually as one moves away from the nucleus, without a sharp cutoff; these are referred to as
atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any ...
s or electron clouds. 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 ( trillionths of a meter), or between 0.3 and 3
ångström The angstromEntry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.m ...
s. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm), and less than 1/1000 of the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tr ...
of visible
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
(400–700 nm). 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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematicall ...
of liquids and solids, the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
of fluids through
molecular sieves A molecular sieve is a material with pores (very small holes) of uniform size. These pore diameters are similar in size to small molecules, and thus large molecules cannot enter or be adsorbed, while smaller molecules can. As a mixture of molec ...
, the arrangement of atoms and ions in
crystal A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macro ...
s, and the size and shape of molecules.


History

In 1920, shortly after it had become possible to determine the sizes of atoms using
X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles ...
, 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 the simplest definition, half the minimum distance between the nuclei of two atoms of the element that are not otherwise bound by covalent or metallic interactions. The Van der Waals radius may be defined even for elements (such as metals) in which Van der Waals forces are dominated by other interactions. Because Van der Waals interactions arise through quantum fluctuations of the atomic polarisation, the polarisability (which can usually be measured or calculated more easily) may be used to define the Van der Waals radius indirectly. * 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 (the
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Inte ...
of the
ionic bond Ionic bonding is a type of chemical bonding that involves the electrostatic attraction between oppositely charged ions, or between two atoms with sharply different electronegativities, and is the primary interaction occurring in ionic compounds ...
between them) 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 (the length of that covalent bond) 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 bond Metallic bonding is a type of chemical bonding that arises from the electrostatic attractive force between conduction electrons (in the form of an electron cloud of delocalized electrons) and positively charged metal ions. It may be des ...
s. *
Bohr radius The Bohr radius (''a''0) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an ...
: the radius of the lowest-energy electron orbit predicted by
Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Syst ...
of the atom (1913). It is only applicable to atoms and ions with a single electron, such as
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-to ...
, singly ionized
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic ta ...
, 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 radius

The following table shows empirically measured covalent radii for the elements, as published by
J. C. Slater John Clarke Slater (December 22, 1900 – July 25, 1976) was a noted American physicist who made major contributions to the theory of the electronic structure of atoms, molecules and solids. He also made major contributions to microwave electroni ...
in 1964. The values are in
picometers The picometre (international spelling as used by the International Bureau of Weights and Measures; SI symbol: pm) or picometer ( American spelling) is a unit of length in the International System of Units (SI), equal to , or one trillionth of ...
(pm or 1×10−12 m), 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 The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of ever ...
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
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s 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 noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under standard conditions, they are all odorless, colorless, monatomic gases with very low ch ...
, the outermost shell is completely filled; therefore, the additional electron of next
alkali metal The alkali metals consist of the chemical elements lithium (Li), sodium (Na), potassium (K),The symbols Na and K for sodium and potassium are derived from their Latin names, ''natrium'' and ''kalium''; these are still the origins of the names ...
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 lanthanide contraction is the greater-than-expected decrease in atomic radii/ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected atomic radii ...
: the 5d block of elements are much smaller than one would expect, due to the weak shielding of the 4f electrons. Essentially, the atomic radius decreases across the periods due to an increasing number of protons. Therefore, there is a greater attraction between the protons and electrons because opposite charges attract, and more protons create a stronger charge. The greater attraction draws the electrons closer to the protons, decreasing the size of the particle. Therefore, the atomic radius decreases. Down the groups, atomic radius increases. This is because there are more energy levels and therefore a greater distance between protons and electrons. In addition, electron shielding causes attraction to decrease, so remaining electrons can go farther away from the positively charged nucleus. Therefore, the size, or atomic radius, increases. 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
lanthanum Lanthanum is a chemical element with the symbol La and atomic number 57. It is a soft, ductile, silvery-white metal that tarnishes slowly when exposed to air. It is the eponym of the lanthanide series, a group of 15 similar elements between l ...
('' Z'' = 57) to ytterbium (''Z'' = 70), are not particularly effective at shielding the increasing nuclear charge from the sub-shells further out. The elements immediately following the
lanthanide The lanthanide () or lanthanoid () series of chemical elements comprises the 15 metallic chemical elements with atomic numbers 57–71, from lanthanum through lutetium. These elements, along with the chemically similar elements scandium and yt ...
s 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 lutetium is in fact slightly smaller than
yttrium Yttrium is a chemical element with the symbol Y and atomic number 39. It is a silvery-metallic transition metal chemically similar to the lanthanides and has often been classified as a " rare-earth element". Yttrium is almost always found in co ...
,
hafnium Hafnium is a chemical element with the symbol Hf and atomic number 72. A lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in many zirconium minerals. Its existence was predicted by Dmitri M ...
has virtually the same atomic radius (and chemistry) as
zirconium Zirconium is a chemical element with the symbol Zr and atomic number 40. The name ''zirconium'' is taken from the name of the mineral zircon, the most important source of zirconium. The word is related to Persian '' zargun'' (zircon; ''zar-gun'' ...
, and
tantalum Tantalum is a chemical element with the symbol Ta and atomic number 73. Previously known as ''tantalium'', it is named after Tantalus, a villain in Greek mythology. Tantalum is a very hard, ductile, lustrous, blue-gray transition metal that ...
has an atomic radius similar to
niobium Niobium is a chemical element with chemical symbol Nb (formerly columbium, Cb) and atomic number 41. It is a light grey, crystalline, and ductile transition metal. Pure niobium has a Mohs hardness rating similar to pure titanium, and it has s ...
, and so forth. The effect of the lanthanide contraction is noticeable up to
platinum Platinum is a chemical element with the symbol Pt and atomic number 78. It is a dense, malleable, ductile, highly unreactive, precious, silverish-white transition metal. Its name originates from Spanish , a diminutive of "silver". Pla ...
(''Z'' = 78), 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, to the point that Yb(OH)3 and Lu(OH)3 can dissolve with difficulty in hot concentrated NaOH. 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 an 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 metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...
s, from
gallium Gallium is a chemical element with the Symbol (chemistry), symbol Ga and atomic number 31. Discovered by France, French chemist Paul-Émile Lecoq de Boisbaudran in 1875, Gallium is in boron group, group 13 of the periodic table and is similar to ...
(''Z'' = 31) to
bromine Bromine is a chemical element with the symbol Br and atomic number 35. It is the third-lightest element in group 17 of the periodic table ( halogens) and is a volatile red-brown liquid at room temperature that evaporates readily to form a simi ...
(''Z'' = 35).


Calculated atomic radius

The following table shows atomic radii computed from theoretical models, as published by
Enrico Clementi Enrico Clementi (November 19, 1931 in Cembra, Italy - March 30, 2021) was an Italian chemist, a pioneer in computational techniques for quantum chemistry and molecular dynamics. Dr. Clementi received his Ph.D. in Chemistry from University of ...
and others in 1967. The values are in picometres (pm).


See also

*
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. ...
* Chemical bond * Covalent radius * Bond length *
Steric hindrance Steric effects arise from the spatial arrangement of atoms. When atoms come close together there is a rise in the energy of the molecule. Steric effects are nonbonding interactions that influence the shape ( conformation) and reactivity of ions ...
*
Kinetic diameter Kinetic diameter is a measure applied to atoms and molecules that expresses the likelihood that a molecule in a gas will collide with another molecule. It is an indication of the size of the molecule as a target. The kinetic diameter is not the s ...


Notes

* Difference between empirical and calculated data: Empirical data 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". In other words, the data are measured through physical observation, and vetted by other experiments generating ''similar results''. Calculated data, on the other hand, are derived from theoretical models. Such predictions are especially useful for elements whose radii cannot be measured experimentally (e.g. those that have not been discovered, or that have too short of a half-life).


References

{{DEFAULTSORT:Atomic Radius Atomic radius Properties of chemical elements