Atomic radius

The atomic radius of a chemical element is a measure of the size of its atoms, usually the mean or typical distance from the center 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. The value of the radius may depend on the atom's state and context.[1]

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 (trillionths of a meter), or between 0.3 and 3 ångströms. Therefore, the radius of an atom is more than 10,000 times the radius of its nucleus (1–10 fm),[2] and less than 1/1000 of the wavelength of visible light (400–700 nm).

Ethanol-3D-vdW
The approximate shape of a molecule of ethanol, CH3CH2OH. Each atom is modeled by a sphere with the element's Van der Waals radius.

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 (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. The atomic radii decrease 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 radius decreases.

Helium atom QM
Diagram of a helium atom, showing the electron probability density as shades of gray.

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.[3] 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.[4]

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.[5]
  • 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 of the ionic bond between them) should equal the sum of their ionic radii.[5]
  • 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.[5]
  • 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 (1913).[6][7] 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 radius

The following table shows empirically measured covalent radii for the elements, as published by J. C. Slater in 1964.[8] The values are in picometers (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.

Group
(column)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period
(row)
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
 
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
 
Cn
 
Nh
 
Fl
 
Mc
 
Lv
 
Ts
 
Og
 
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
 

Explanation of the general trends

Atomic number to radius graph
A graph comparing the atomic radius of elements with atomic numbers 1–100. Accuracy of ±5 pm.

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.

Essentially, 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 creates a stronger charge. The greater attraction draws the electrons closer to the protons, decreasing the size of the particle. Therefore, 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, size (atomic radius) increases.

The following table summarizes the main phenomena that influence the atomic radius of an element:

factor principle increase with... tend to effect on radius
electron shells quantum mechanics principal and azimuthal quantum numbers increase atomic radius increases down each column
nuclear charge attractive force acting on electrons by protons in nucleus atomic number decrease atomic radius decreases along each period
shielding repulsive force acting on outermost shell electrons by inner electrons number of electrons in inner shells increase atomic radius reduces the effect of the 2nd factor

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.[9] 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.

Due to lanthanide contraction, the 5 following observations can be drawn:

  1. 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+.
  2. There is a regular decrease in their ionic radii.
  3. There is a regular decrease in their tendency to act as a reducing agent, with increase in atomic number.
  4. The second and third rows of d-block transition elements are quite close in properties.
  5. 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 (Z = 31) to bromine (Z = 35).[9]

Calculated atomic radii

The following table shows atomic radii computed from theoretical models, as published by Enrico Clementi and others in 1967.[10] The values are in picometres (pm).

Group
(column)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Period
(row)
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
127
Rn
120
7 Fr
 
Ra
 
**
 
Rf
 
Db
 
Sg
 
Bh
 
Hs
 
Mt
 
Ds
 
Rg
 
Cn
 
Nh
 
Fl
 
Mc
 
Lv
 
Ts
 
Og
 
Lanthanides *
 
La
226
Ce
210
Pr
247
Nd
206
Pm
205
Sm
238
Eu
231
Gd
233
Tb
225
Dy
228
Ho
226
Er
226
Tm
222
Yb
222
Lu
217
Actinides **
 
Ac
 
Th
 
Pa
 
U
 
Np
 
Pu
 
Am
 
Cm
 
Bk
 
Cf
 
Es
 
Fm
 
Md
 
No
 
Lr
 

See also

References

  1. ^ Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). Wiley. p. 1385. ISBN 978-0-471-84997-1.
  2. ^ Basdevant, J.-L.; Rich, J.; Spiro, M. (2005). Fundamentals in Nuclear Physics. Springer. p. 13, fig 1.1. ISBN 978-0-387-01672-6.
  3. ^ Bragg, W. L. (1920). "The arrangement of atoms in crystals". Philosophical Magazine. 6. 40 (236): 169–189. doi:10.1080/14786440808636111.
  4. ^ Wyckoff, R. W. G. (1923). "On the Hypothesis of Constant Atomic Radii". Proceedings of the National Academy of Sciences of the United States of America. 9 (2): 33–38. Bibcode:1923PNAS....9...33W. doi:10.1073/pnas.9.2.33. PMC 1085234. PMID 16576657.
  5. ^ a b c Pauling, L. (1945). The Nature of the Chemical Bond (2nd ed.). Cornell University Press. LCCN 42034474.
  6. ^ Bohr, N. (1913). "On the Constitution of Atoms and Molecules, Part I. – Binding of Electrons by Positive Nuclei" (PDF). Philosophical Magazine. 6. 26 (151): 1–24. doi:10.1080/14786441308634955. Retrieved 8 June 2011.
  7. ^ Bohr, N. (1913). "On the Constitution of Atoms and Molecules, Part II. – Systems containing only a Single Nucleus" (PDF). Philosophical Magazine. 6. 26 (153): 476–502. doi:10.1080/14786441308634993. Retrieved 8 June 2011.
  8. ^ Slater, J. C. (1964). "Atomic Radii in Crystals". Journal of Chemical Physics. 41 (10): 3199–3205. Bibcode:1964JChPh..41.3199S. doi:10.1063/1.1725697.
  9. ^ a b Jolly, W. L. (1991). Modern Inorganic Chemistry (2nd ed.). McGraw-Hill. p. 22. ISBN 978-0-07-112651-9.
  10. ^ Clementi, E.; Raimond, D. L.; Reinhardt, W. P. (1967). "Atomic Screening Constants from SCF Functions. II. Atoms with 37 to 86 Electrons". Journal of Chemical Physics. 47 (4): 1300–1307. Bibcode:1967JChPh..47.1300C. doi:10.1063/1.1712084.
Alkali metal

The alkali metals are a group (column) in the periodic table consisting of the chemical elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb), caesium (Cs), and francium (Fr). This group lies in the s-block of the periodic table of elements as all alkali metals have their outermost electron in an s-orbital: this shared electron configuration results in their having very similar characteristic properties. Indeed, the alkali metals provide the best example of group trends in properties in the periodic table, with elements exhibiting well-characterised homologous behaviour.

The alkali metals are all shiny, soft, highly reactive metals at standard temperature and pressure and readily lose their outermost electron to form cations with charge +1. They can all be cut easily with a knife due to their softness, exposing a shiny surface that tarnishes rapidly in air due to oxidation by atmospheric moisture and oxygen (and in the case of lithium, nitrogen). Because of their high reactivity, they must be stored under oil to prevent reaction with air, and are found naturally only in salts and never as the free elements. Caesium, the fifth alkali metal, is the most reactive of all the metals. In the modern IUPAC nomenclature, the alkali metals comprise the group 1 elements, excluding hydrogen (H), which is nominally a group 1 element but not normally considered to be an alkali metal as it rarely exhibits behaviour comparable to that of the alkali metals. All the alkali metals react with water, with the heavier alkali metals reacting more vigorously than the lighter ones.

All of the discovered alkali metals occur in nature as their compounds: in order of abundance, sodium is the most abundant, followed by potassium, lithium, rubidium, caesium, and finally francium, which is very rare due to its extremely high radioactivity; francium occurs only in the minutest traces in nature as an intermediate step in some obscure side branches of the natural decay chains. Experiments have been conducted to attempt the synthesis of ununennium (Uue), which is likely to be the next member of the group, but they have all met with failure. However, ununennium may not be an alkali metal due to relativistic effects, which are predicted to have a large influence on the chemical properties of superheavy elements; even if it does turn out to be an alkali metal, it is predicted to have some differences in physical and chemical properties from its lighter homologues.

Most alkali metals have many different applications. One of the best-known applications of the pure elements is the use of rubidium and caesium in atomic clocks, of which caesium atomic clocks are the most accurate and precise representation of time. A common application of the compounds of sodium is the sodium-vapour lamp, which emits light very efficiently. Table salt, or sodium chloride, has been used since antiquity. Lithium finds use as a psychiatric medication. Sodium and potassium are also essential elements, having major biological roles as electrolytes, and although the other alkali metals are not essential, they also have various effects on the body, both beneficial and harmful.

Atomic nucleus

The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron in 1932, models for a nucleus composed of protons and neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. An atom is composed of a positively-charged nucleus, with a cloud of negatively-charged electrons surrounding it, bound together by electrostatic force. Almost all of the mass of an atom is located in the nucleus, with a very small contribution from the electron cloud. Protons and neutrons are bound together to form a nucleus by the nuclear force.

The diameter of the nucleus is in the range of 1.7566 fm (1.7566×10−15 m) for hydrogen (the diameter of a single proton) to about 11.7142 fm for the heaviest atom uranium. These dimensions are much smaller than the diameter of the atom itself (nucleus + electron cloud), by a factor of about 26,634 (uranium atomic radius is about 156 pm (156×10−12 m)) to about 60,250 (hydrogen atomic radius is about 52.92 pm).The branch of physics concerned with the study and understanding of the atomic nucleus, including its composition and the forces which bind it together, is called nuclear physics.

Atomic radii of the elements (data page)

The atomic radius of a chemical element is the distance from the centre of the nucleus to the outermost shell of the 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.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.

Bismuth Indium

The elements bismuth and indium have relatively low melting points when compared to other metals, and their alloy Bismuth Indium is classified as a fusible alloy. It has a melting point lower than the eutectic point of the tin lead alloy. The most common application of the alloy is as a low temperature solder, which can also contain, besides Bismuth and Indium, lead, cadmium and tin.

Bulk modulus

The bulk modulus ( or ) of a substance is a measure of how resistant to compression that substance is. It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume. Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear, and Young's modulus describes the response to linear stress. For a fluid, only the bulk modulus is meaningful. For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.

Core charge

Core charge is the effective nuclear charge experienced by an outer shell electron. In other words, core charge is an expression of the attractive force experienced by the valence electrons to the core of an atom which takes into account the shielding effect of core electrons. Core charge can be calculated by taking the number of protons in the nucleus minus the number of core electrons, also called inner shell electrons, and is always a positive value.

Core charge is a convenient way of explaining trends in the periodic table. Since the core charge increases as you move across a row of the periodic table, the outer-shell electrons are pulled more and more strongly towards the nucleus and the atomic radius decreases. This can be used to explain a number of periodic trends such as atomic radius, first ionization energy (IE), electronegativity, and oxidizing.

Core charge can also be calculated as 'atomic number' minus 'all electrons except those in the outer shell'. For example, chlorine (element 17), with electron configuration 1s2 2s2 2p6 3s2 3p5, has 17 protons and 10 inner shell electrons (2 in the first shell, and 8 in the second) so:

Core charge = 17 − 10 = +7A core charge is the net charge of a nucleus, considering the completed shells of electrons to act as a 'shield.' As a core charge increases, the valence electrons are more strongly attracted to the nucleus, and the atomic radius decreases across the period.

Covalent radius of fluorine

The covalent radius of fluorine is a measure of the size of a fluorine atom; it is approximated at about 60 picometres.

Since fluorine is a relatively small atom with a large electronegativity, its covalent radius is difficult to evaluate. The covalent radius is defined as half the bond lengths between two neutral atoms of the same kind connected with a single bond. By this definition, the covalent radius of F is 71 pm. However, the F-F bond in F2 is abnormally weak and long. Besides, almost all bonds to fluorine are highly polar because of its large electronegativity, so the use of a covalent radius to predict the length of such a bond is inadequate and the bond lengths calculated from these radii are almost always longer than the experimental values.

Bonds to fluorine have considerable ionic character, a result of its small atomic radius and large electronegativity. Therefore, the bond length of F is influenced by its ionic radius, the size of ions in an ionic crystal, which is about 133 pm for fluoride ions. The ionic radius of fluoride is much larger than its covalent radius. When F becomes F−, it gains one electron but has the same number of protons, meaning the attraction of the protons to the electrons is weaker, and the radius is larger.

Isoelectronicity

Isoelectronicity is the phenomenon of two or more chemical species (atoms, molecules, radicals, ions etc.) differing in the atoms of which they are formed but having the same number of valence electrons and the same structure (that is, the same number of atoms with the same connectivity). The species concerned are termed isoelectronic.

This definition is sometimes termed valence isoelectronicity, in contrast with various alternatives. At one extreme these require identity of the total electron count and with it the entire electron configuration. More usually, alternatives are broader, and may extend to allowing different numbers of atoms in the species being compared.The importance of the concept lies in identifying significantly related species, as pairs or series. Isoelectronic species can be expected to show useful consistency and predictability in their properties. (Slight differences of, for example, structural formula, such as a double versus single bond, commonly have major effects.)

Electron-density calculations have been performed on many common substances, resulting in reaction predictions. Identifying a new, rare or odd compound as isoelectronic with one already characterised offers clues to possible properties and reactions.

Lanthanide contraction

The lanthanide contraction is the greater-than-expected decrease in ionic radii of the elements in the lanthanide series from atomic number 57, lanthanum, to 71, lutetium, which results in smaller than otherwise expected ionic radii for the subsequent elements starting with 72, hafnium. The term was coined by the Norwegian geochemist Victor Goldschmidt in his series "Geochemische Verteilungsgesetze der Elemente".

Lead shielding

Lead shielding refers to the use of lead as a form of radiation protection to shield people or objects from radiation so as to reduce the effective dose. Lead can effectively attenuate certain kinds of radiation because of its high density and high atomic number; principally, it is effective at stopping gamma rays and x-rays.

Light metal

A light metal is any metal of relatively low density. More specific definitions have been proposed; none have obtained widespread acceptance. Magnesium, aluminium and titanium are light metals of significant commercial importance. Their densities of 1.7, 2.7 and 4.5 g/cm3 range from 19 to 56% of the densities of the older structural metals, iron (7.9) and copper (8.9).

List of data references for chemical elements

Values for many properties of the elements, together with various references, are collected on these data pages.

Miedema's model

Miedema's model is a semi-empirical approach for estimating the heat of formation of solid or liquid metal alloys and /or compounds in the framework of thermodynamic calculations for metals and minerals. It was developed by the Dutch scientist Andries Rinse Miedema ( 15 November 1933 - 28 May 1992 ) while working at Philips Research Laboratories Philips_Natuurkundig_Laboratorium. It may provide or confirm basic enthalpy data that have always been needed for the calculation of phase diagrams of metals, and that are now currently approached by CALPHAD. The method has been introduced by Miedema in a couple of papers appeared in 1973 in Philips Technical Review Magazine entitled "A simple model for alloys". While Miedema himself or with collaborators produced many scientific papers we report here in his own words the genuine motivation of his approach "Reliable rules for the alloying behaviour of metals have long been sought. There is the qualitative rule that states that the greater the difference in the electronegativity of two metals, the greater the heat of formation - and hence the stability. Then there is the Hume-Rothery rule, which states that two metals that differ by more than 15% in their atomic radius will not form substitutional solid solutions. This rule can only be used reliably (90 % success) to predict poor solubility; it cannot predict good solubility. The author has proposed a simple atomic model, which is empirical like the other two rules, but nevertheless has a clear physical basis and predicts the alloying behaviour of transition metals accurately in 98 % of cases. The model is very suitable for graphical presentation of the data and is therefore easy to use in practice." There are several free web bases applications like Entall or Miedema Calculator. The latter has been recently reviewed and improved, with an extension of the method in a scientific publication. A simple presentation of the method is in the appendix B of the book, while the original Algol program has been ported in a fortran code

Periodic table

The periodic table, also known as the periodic table of elements, is a tabular display of the chemical elements, which are arranged by atomic number, electron configuration, and recurring chemical properties. The structure of the table shows periodic trends. The seven rows of the table, called periods, generally have metals on the left and non-metals on the right. The columns, called groups, contain elements with similar chemical behaviours. Six groups have accepted names as well as assigned numbers: for example, group 17 elements are the halogens; and group 18 are the noble gases. Also displayed are four simple rectangular areas or blocks associated with the filling of different atomic orbitals.

The organization of the periodic table can be used to derive relationships between the various element properties, and also to predict chemical properties and behaviours of undiscovered or newly synthesized elements. Russian chemist Dmitri Mendeleev published the first recognizable periodic table in 1869, developed mainly to illustrate periodic trends of the then-known elements. He also predicted some properties of unidentified elements that were expected to fill gaps within the table. Most of his forecasts proved to be correct. Mendeleev's idea has been slowly expanded and refined with the discovery or synthesis of further new elements and the development of new theoretical models to explain chemical behaviour. The modern periodic table now provides a useful framework for analyzing chemical reactions, and continues to be widely used in chemistry, nuclear physics and other sciences.

The elements from atomic numbers 1 (hydrogen) through 118 (oganesson) have been discovered or synthesized, completing seven full rows of the periodic table. The first 94 elements all occur naturally, though some are found only in trace amounts and a few were discovered in nature only after having first been synthesized. Elements 95 to 118 have only been synthesized in laboratories or nuclear reactors. The synthesis of elements having higher atomic numbers is currently being pursued: these elements would begin an eighth row, and theoretical work has been done to suggest possible candidates for this extension. Numerous synthetic radionuclides of naturally occurring elements have also been produced in laboratories.

Periodic trends

Periodic trends are specific patterns in the properties of chemical elements that are revealed in the periodic table of elements. Major periodic trends include electronegativity, ionization energy, electron affinity, atomic radius, ionic radius, metallic character, and chemical reactivity.

Periodic trends arise from the changes in the atomic structure of the chemical elements within their respective periods (horizontal rows) and groups in the periodic table. These trends enable the chemical elements to be organized in the periodic table based on their atomic structures and properties.

Some exceptions to these trends exist, such as that of ionization energy in Groups 3 and 6.

Picometre

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 metric system, equal to 1×10−12 m, or one trillionth (1/1000000000000) of a metre, which is the SI base unit of length.

The picometre is one thousandth of a nanometre, one millionth of a micrometre (also known as a micron), and used to be called micromicron, stigma, or bicron. The symbol µµ was once used for it. It is also one hundredth of an Ångström, an internationally recognised (but non-SI) unit of length.

Ronald Gillespie

Ronald James Gillespie, (born August 21, 1924 in London), a chemistry professor at McMaster University, specializes in the field of Molecular Geometry in Chemistry. In 2007 he was awarded the Order of Canada.He was educated at the University of London obtaining a B.Sc in 1945, a Ph.D in 1949 and a D.Sc in 1957. He was Assistant Lecturer and then Lecturer in the Department of Chemistry at University College London in England from 1950 to 1958. He moved to McMaster University, Hamilton, Ontario, Canada in 1958 and is now emeritus professor. He was elected as a Fellow of the Royal Society of Canada in 1965 and a Fellow of the Royal Society of London in 1977.

Gillespie has done extensive work on expanding the idea of the Valence Shell Electron Pair Repulsion (VSEPR) model of Molecular Geometry, which he developed with Ronald Nyholm (and thus is also known as the Gillespie-Nyholm theory), and setting the rules for assigning numbers. He has written several books on this VSEPR topic in chemistry. With other workers he developed LCP theory, (ligand close packing theory), which for some molecules allows geometry to be predicted on the basis of ligand-ligand repulsions. Gillespie has also done extensive work on interpreting the covalent radius of fluorine. The covalent radius of most atoms is found by taking half the length of a single bond between two similar atoms in a neutral molecule. Calculating the covalent radius for fluorine is more difficult because of its high electronegativity compared to its small atomic radius size. Ronald Gillespie’s work on the bond length of fluorine focuses on theoretically determining the covalent radius of fluorine by examining its covalent radius when it is attached to several different atoms.

Ångström

The ångström (,ANG-strəm; ANG-strum Swedish: [²ɔŋːstrœm]) or angstrom is a unit of length equal to 10−10 m (one ten-billionth of a metre) or 0.1 nanometre. Its symbol is Å, a letter in the Swedish alphabet.

The natural sciences and technology often use ångström to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. Atoms of phosphorus, sulfur, and chlorine are about an ångström in covalent radius, while a hydrogen atom is about half an ångström; see atomic radius. Visible light has wavelengths in the range of 4000–7000 Å.

The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The symbol is always written with the Swedish alphabet letter 'Å'. Though it appears to be of the Latin alphabet 'A' with a ring diacritic, it is not. The unit's name is often written in English with the Latin alphabet 'A', but the official definition is the Swedish letter 'Å'. It is not a part of the SI system of units, but it can be considered part of the metric system.

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