Periodic table: Difference between revisions

From Wikipedia, the free encyclopedia
Content deleted Content added
m Reverted edits by 66.208.211.154 to last revision by Martin451 (HG)
Edwin
Line 53: Line 53:
The elements ununbium, ununtrium, ununquadium, etc. are elements that have been discovered, but so far have not received a [[trivial name]] yet. There is a [[Systematic element name|system]] for naming them temporarily.
The elements ununbium, ununtrium, ununquadium, etc. are elements that have been discovered, but so far have not received a [[trivial name]] yet. There is a [[Systematic element name|system]] for naming them temporarily.


EDWIN
==Classification==
===Groups===
{{Main|Group (periodic table)}}
A ''group'' or ''family'' is a vertical column in the periodic table. Groups are considered the most important method of classifying the elements. In some groups, the elements have very similar properties and exhibit a clear trend in properties down the group. These groups tend to be given trivial (unsystematic) names, e.g., the [[alkali metal]]s, [[alkaline earth metals]], [[halogen]]s, [[pnictogen]]s, [[chalcogen]]s, and [[noble gas]]es. Some other groups in the periodic table display fewer similarities and/or vertical trends (for example Group 14), and these have no trivial names and are referred to simply by their group numbers.

===Periods===
{{Main|Period (periodic table)}}
A ''period'' is a horizontal row in the periodic table. Although groups are the most common way of classifying elements, there are some regions of the periodic table where the horizontal trends and similarities in properties are more significant than vertical group trends. This can be true in the [[d-block]] (or "[[transition metal]]s"), and especially for the [[f-block]], where the [[lanthanoids]] and [[actinoids]] form two substantial horizontal series of elements.

===Blocks===
{{Main|Periodic table block}}
[[File:PTable structure.png|thumb|This diagram shows the [[periodic table block]]s.]]
Because of the importance of the outermost shell, the different regions of the periodic table are sometimes referred to as ''[[periodic table block]]s'', named according to the [[subshell]] in which the "last" electron resides. The [[s-block]] comprises the first two groups ([[alkali metal]]s and [[alkaline earth metals]]) as well as [[hydrogen]] and [[helium]]. The [[p-block]] comprises the last six groups (groups 13 through 18) and contains, among others, all of the [[semimetals]]. The [[d-block]] comprises groups 3 through 12 and contains all of the [[transition metal]]s. The [[f-block]], usually offset below the rest of the periodic table, comprises the [[rare earth metal]]s.

===Other===
The chemical elements are also grouped together in other ways. Some of these groupings are often illustrated on the periodic table, such as [[transition metal]]s, [[poor metal]]s, and [[metalloid]]s. Other informal groupings exist, such as the [[platinum group]] and the [[noble metals]].


==Periodicity of chemical properties==
==Periodicity of chemical properties==

Revision as of 21:16, 6 January 2010

The periodic table of the chemical elements (also Mendeleev's table, periodic table of the elements or just periodic table) is a tabular display of the chemical elements. Although precursors to this table exist, its invention is generally credited to Russian chemist Dmitri Mendeleev in 1869, who intended the table to illustrate recurring ("periodic") trends in the properties of the elements. The layout of the table has been refined and extended over time, as new elements have been discovered, and new theoretical models have been developed to explain chemical behavior.[1]

The periodic table is now ubiquitous within the academic discipline of chemistry, providing an extremely useful framework to classify, systematize, and compare all of the many different forms of chemical behavior. The table has found wide application in chemistry, physics, biology, and engineering, especially chemical engineering. The current standard table contains 117 elements as of July 2009 (elements 1116 and element 118).

Structure of the periodic table

The periodic table of the chemical elements (also Mendeleev's table, periodic table of the elements or just periodic table) is a tabular display of the chemical elements. Although precursors to this table exist, its invention is generally credited to Russian chemist Dmitri Mendeleev in 1869, who intended the table to illustrate recurring ("periodic") trends in the properties of the elements. The layout of the table has been refined and extended over time, as new elements have been discovered, and new theoretical models have been developed to explain chemical behavior.[2]

The periodic table is now ubiquitous within the academic discipline of chemistry, providing an extremely useful framework to classify, systematize, and compare all of the many different forms of chemical behavior. The table has found wide application in chemistry, physics, biology, and engineering, especially chemical engineering. The current standard table contains 117 elements as of July 2009 (elements 1116 and element 118).

Structure of the periodic table

       Template loop detected: Periodic table (standard)

Other alternative periodic tables exist.

Some versions of the table show a dark stair-step line along the metalloids. Metals are to the left of the line and non-metals to the right.[3]

The layout of the periodic table demonstrates recurring ("periodic") chemical properties. Elements are listed in order of increasing atomic number (i.e., the number of protons in the atomic nucleus). Rows are arranged so that elements with similar properties fall into the same columns (groups or families). According to quantum mechanical theories of electron configuration within atoms, each row (period) in the table corresponded to the filling of a quantum shell of electrons. There are progressively longer periods further down the table, grouping the elements into s-, p-, d- and f-blocks to reflect their electron configuration.

In printed tables, each element is usually listed with its element symbol and atomic number; many versions of the table also list the element's atomic mass and other information, such as its abbreviated electron configuration, electronegativity and most common valence numbers.

As of 2006, the table contains 117 chemical elements whose discoveries have been confirmed. Ninety-four are found naturally on Earth, and the rest are synthetic elements that have been produced artificially in particle accelerators. Elements 43 (technetium), 61 (promethium) and all elements greater than 83 (bismuth), beginning with 84 (polonium) have no stable isotopes. The atomic mass of each of these element's isotope having the longest half-life is typically reported on periodic tables with parentheses.[4] Isotopes of elements 43, 61, 93 (neptunium) and 94 (plutonium), first discovered synthetically, have since been discovered in trace amounts on Earth as products of natural radioactive decay processes.

The primary determinant of an element's chemical properties is its electron configuration, particularly the valence shell electrons. For instance, any atoms with four valence electrons occupying p orbitals will exhibit some similarity. The type of orbital in which the atom's outermost electrons reside determines the "block" to which it belongs. The number of valence shell electrons determines the family, or group, to which the element belongs.

The total number of electron shells an atom has determines the period to which it belongs. Each shell is divided into different subshells, which as atomic number increases are filled in roughly this order (the Aufbau principle):

Subshell: S G F D P
Period
1 1s
2 2s 2p
3 3s 3p
4 4s 3d 4p
5 5s 4d 5p
6 6s 4f 5d 6p
7 7s 5f 6d 7p
8 8s 5g 6f 7d 8p

Hence the structure of the table. Since the outermost electrons determine chemical properties, those with the same number of valence electrons are grouped together.

Progressing through a group from lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus. For instance, the outer-shell (or "valence") electrons of the first group, headed by hydrogen, all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. As another example, both carbon and lead have four electrons in their outer shell orbitals.

Note that as atomic number (i.e., charge on the atomic nucleus) increases, this leads to greater spin-orbit coupling between the nucleus and the electrons, reducing the validity of the quantum mechanical orbital approximation model, which considers each atomic orbital as a separate entity.

The elements ununbium, ununtrium, ununquadium, etc. are elements that have been discovered, but so far have not received a trivial name yet. There is a system for naming them temporarily.

EDWIN

Periodicity of chemical properties

The main value of the periodic table is the ability to predict the chemical properties of an element based on its location on the table. It should be noted that the properties vary differently when moving vertically along the columns of the table than when moving horizontally along the rows.

Periodic trends of groups

Modern quantum mechanical theories of atomic structure explain group trends by proposing that elements within the same group have the same electron configurations in their valence shell, which is the most important factor in accounting for their similar properties. Elements in the same group also show patterns in their atomic radius, ionization energy, and electronegativity. From top to bottom in a group, the atomic radii of the elements increase. Since there are more filled energy levels, valence electrons are found farther from the nucleus. From the top, each successive element has a lower ionization energy because it is easier to remove an electron since the atoms are less tightly bound. Similarly, a group will also see a top to bottom decrease in electronegativity due to an increasing distance between valence electrons and the nucleus.

Periodic trends of periods

Periodic trend for ionization energy. Each period begins at a minimum for the alkali metals, and ends at a maximum for the noble gases.

Elements in the same period show trends in atomic radius, ionization energy, electron affinity, and electronegativity. Moving left to right across a period, atomic radius usually decreases. This occurs because each successive element has an added proton and electron which causes the electron to be drawn closer to the nucleus. This decrease in atomic radius also causes the ionization energy to increase when moving from left to right across a period. The more tightly bound an element is, the more energy is required to remove an electron. Similarly, electronegativity will increase in the same manner as ionization energy because of the amount of pull that is exerted on the electrons by the nucleus. Electron affinity also shows a slight trend across a period. Metals (left side of a period) generally have a lower electron affinity than nonmetals (right side of a period) with the exception of the noble gases.

History

In 1789, Antoine Lavoisier published a list of 33 chemical elements. Although Lavoisier grouped the elements into gases, metals, non-metals, and earths, chemists spent the following century searching for a more precise classification scheme. In 1829, Johann Wolfgang Döbereiner observed that many of the elements could be grouped into triads (groups of three) based on their chemical properties. Lithium, sodium, and potassium, for example, were grouped together as being soft, reactive metals. Döbereiner also observed that, when arranged by atomic weight, the second member of each triad was roughly the average of the first and the third.[5] This became known as the Law of triads.[citation needed] German chemist Leopold Gmelin worked with this system, and by 1843 he had identified ten triads, three groups of four, and one group of five. Jean Baptiste Dumas published work in 1857 describing relationships between various groups of metals. Although various chemists were able to identify relationships between small groups of elements, they had yet to build one scheme that encompassed them all.[5]

German chemist August Kekulé had observed in 1858 that carbon has a tendency to bond with other elements in a ratio of one to four. Methane, for example, has one carbon atom and four hydrogen atoms. This concept eventually became known as valency. In 1864, fellow German chemist Julius Lothar Meyer published a table of the 49 known elements arranged by valency. The table revealed that elements with similar properties often shared the same valency.[6]

English chemist John Newlands published a series of papers in 1864 and 1865 that described his attempt at classifying the elements: When listed in order of increasing atomic weight, similar physical and chemical properties recurred at intervals of eight, which he likened to the octaves of music.[7][8] This law of octaves, however, was ridiculed by his contemporaries.[9]

Portrait of Dmitri Mendeleev

Russian chemistry professor Dmitri Ivanovich Mendeleev and Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively. They both constructed their tables in a similar manner: by listing the elements in a row or column in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.[10] The success of Mendeleev's table came from two decisions he made: The first was to leave gaps in the table when it seemed that the corresponding element had not yet been discovered.[11] Mendeleev was not the first chemist to do so, but he went a step further by using the trends in his periodic table to predict the properties of those missing elements, such as gallium and germanium.[12] The second decision was to occasionally ignore the order suggested by the atomic weights and switch adjacent elements, such as cobalt and nickel, to better classify them into chemical families. With the development of theories of atomic structure, it became apparent that Mendeleev had inadvertently listed the elements in order of increasing atomic number.[13]

With the development of modern quantum mechanical theories of electron configurations within atoms, it became apparent that each row (or period) in the table corresponded to the filling of a quantum shell of electrons. In Mendeleev's original table, each period was the same length. However, because larger atoms have more electron sub-shells, modern tables have progressively longer periods further down the table.[14]

In the years that followed after Mendeleev published his periodic table, the gaps he left were filled as chemists discovered more chemical elements. The last naturally-occurring element to be discovered was Francium (referred to by Mendeleev as eka-caesium) in 1939.[15] The periodic table has also grown with the addition of synthetic and transuranic elements. The first transuranic element to be discovered was neptunium, which was formed by bombarding uranium with neutrons in a cyclotron in 1939.[16]

See also

Notes

  1. ^ IUPAC article on periodic table
  2. ^ IUPAC article on periodic table
  3. ^ Science Standards of Learning Curriculum Framework
  4. ^ Dynamic periodic table
  5. ^ a b Ball, p. 100
  6. ^ Ball, p. 101
  7. ^ Newlands, John A. R. (1864-08-20). "On Relations Among the Equivalents". Chemical News. 10: 94–95.
  8. ^ Newlands, John A. R. (1865-08-18). "On the Law of Octaves". Chemical News. 12: 83.
  9. ^ Bryson, Bill (2004). A Short History of Nearly Everything. London: Black Swan. pp. 141–142. ISBN 9780552151740.
  10. ^ Ball, pp. 100–102
  11. ^ Pullman, p. 227
  12. ^ Ball, p. 105
  13. ^ Atkins, p. 87
  14. ^ Ball, p. 111
  15. ^ Adloff, Jean-Pierre; Kaufman, George B. (2005-09-25). Francium (Atomic Number 87), the Last Discovered Natural Element. The Chemical Educator 10 (5). Retrieved on 2007-03-26.
  16. ^ Ball, p. 123

References

  • Atkins, P. W. (1995). The Periodic Kingdom. HarperCollins Publishers, Inc. ISBN 0-465-07265-8.
  • Ball, Philip (2002). The Ingredients: A Guided Tour of the Elements. Oxford University Press. ISBN 0-19-284100-9.
  • Brown, Theodore L.; LeMay, H. Eugene; Bursten, Bruce E. (2005). Chemistry:The Central Science (10th ed.). Prentice Hall. ISBN 0-13-109686-9.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Pullman, Bernard (1998). The Atom in the History of Human Thought. Translated by Axel Reisinger. Oxford University Press. ISBN 0-19-515040-6.

Further reading

Template:Unlinkedrefs

  • Bouma, J. (1989). "An Application-Oriented Periodic Table of the Elements". J. Chem. Ed. 66: 741.
  • Eric Scerri (2007). The periodic table: its story and its significance. Oxford [Oxfordshire]: Oxford University Press. ISBN 0-19-530573-6.
  • Imyanitov, N.S. (1999). "Mathematical description of dialectic regular trends in the periodic system". Russ. J. Gen. Chem. 69: 509.
  • Imyanitov, N.S. (2003). "Modification of Various Functions for Description of Periodic Dependences". Russ. J. Coord. Chem. 29: 46. doi:10.1023/A:1021895001562.
  • Mazurs, E.G (1974). Graphical Representations of the Periodic System During One Hundred Years. Alabama: University of Alabama Press.

External links

Template:Link FL

Other alternative periodic tables exist.

Some versions of the table show a dark stair-step line along the metalloids. Metals are to the left of the line and non-metals to the right.[1]

The layout of the periodic table demonstrates recurring ("periodic") chemical properties. Elements are listed in order of increasing atomic number (i.e., the number of protons in the atomic nucleus). Rows are arranged so that elements with similar properties fall into the same columns (groups or families). According to quantum mechanical theories of electron configuration within atoms, each row (period) in the table corresponded to the filling of a quantum shell of electrons. There are progressively longer periods further down the table, grouping the elements into s-, p-, d- and f-blocks to reflect their electron configuration.

In printed tables, each element is usually listed with its element symbol and atomic number; many versions of the table also list the element's atomic mass and other information, such as its abbreviated electron configuration, electronegativity and most common valence numbers.

As of 2006, the table contains 117 chemical elements whose discoveries have been confirmed. Ninety-four are found naturally on Earth, and the rest are synthetic elements that have been produced artificially in particle accelerators. Elements 43 (technetium), 61 (promethium) and all elements greater than 83 (bismuth), beginning with 84 (polonium) have no stable isotopes. The atomic mass of each of these element's isotope having the longest half-life is typically reported on periodic tables with parentheses.[2] Isotopes of elements 43, 61, 93 (neptunium) and 94 (plutonium), first discovered synthetically, have since been discovered in trace amounts on Earth as products of natural radioactive decay processes.

The primary determinant of an element's chemical properties is its electron configuration, particularly the valence shell electrons. For instance, any atoms with four valence electrons occupying p orbitals will exhibit some similarity. The type of orbital in which the atom's outermost electrons reside determines the "block" to which it belongs. The number of valence shell electrons determines the family, or group, to which the element belongs.

The total number of electron shells an atom has determines the period to which it belongs. Each shell is divided into different subshells, which as atomic number increases are filled in roughly this order (the Aufbau principle):

Subshell: S G F D P
Period
1 1s
2 2s 2p
3 3s 3p
4 4s 3d 4p
5 5s 4d 5p
6 6s 4f 5d 6p
7 7s 5f 6d 7p
8 8s 5g 6f 7d 8p

Hence the structure of the table. Since the outermost electrons determine chemical properties, those with the same number of valence electrons are grouped together.

Progressing through a group from lightest element to heaviest element, the outer-shell electrons (those most readily accessible for participation in chemical reactions) are all in the same type of orbital, with a similar shape, but with increasingly higher energy and average distance from the nucleus. For instance, the outer-shell (or "valence") electrons of the first group, headed by hydrogen, all have one electron in an s orbital. In hydrogen, that s orbital is in the lowest possible energy state of any atom, the first-shell orbital (and represented by hydrogen's position in the first period of the table). In francium, the heaviest element of the group, the outer-shell electron is in the seventh-shell orbital, significantly further out on average from the nucleus than those electrons filling all the shells below it in energy. As another example, both carbon and lead have four electrons in their outer shell orbitals.

Note that as atomic number (i.e., charge on the atomic nucleus) increases, this leads to greater spin-orbit coupling between the nucleus and the electrons, reducing the validity of the quantum mechanical orbital approximation model, which considers each atomic orbital as a separate entity.

The elements ununbium, ununtrium, ununquadium, etc. are elements that have been discovered, but so far have not received a trivial name yet. There is a system for naming them temporarily.

EDWIN

Periodicity of chemical properties

The main value of the periodic table is the ability to predict the chemical properties of an element based on its location on the table. It should be noted that the properties vary differently when moving vertically along the columns of the table than when moving horizontally along the rows.

Periodic trends of groups

Modern quantum mechanical theories of atomic structure explain group trends by proposing that elements within the same group have the same electron configurations in their valence shell, which is the most important factor in accounting for their similar properties. Elements in the same group also show patterns in their atomic radius, ionization energy, and electronegativity. From top to bottom in a group, the atomic radii of the elements increase. Since there are more filled energy levels, valence electrons are found farther from the nucleus. From the top, each successive element has a lower ionization energy because it is easier to remove an electron since the atoms are less tightly bound. Similarly, a group will also see a top to bottom decrease in electronegativity due to an increasing distance between valence electrons and the nucleus.

Periodic trends of periods

Periodic trend for ionization energy. Each period begins at a minimum for the alkali metals, and ends at a maximum for the noble gases.

Elements in the same period show trends in atomic radius, ionization energy, electron affinity, and electronegativity. Moving left to right across a period, atomic radius usually decreases. This occurs because each successive element has an added proton and electron which causes the electron to be drawn closer to the nucleus. This decrease in atomic radius also causes the ionization energy to increase when moving from left to right across a period. The more tightly bound an element is, the more energy is required to remove an electron. Similarly, electronegativity will increase in the same manner as ionization energy because of the amount of pull that is exerted on the electrons by the nucleus. Electron affinity also shows a slight trend across a period. Metals (left side of a period) generally have a lower electron affinity than nonmetals (right side of a period) with the exception of the noble gases.

History

In 1789, Antoine Lavoisier published a list of 33 chemical elements. Although Lavoisier grouped the elements into gases, metals, non-metals, and earths, chemists spent the following century searching for a more precise classification scheme. In 1829, Johann Wolfgang Döbereiner observed that many of the elements could be grouped into triads (groups of three) based on their chemical properties. Lithium, sodium, and potassium, for example, were grouped together as being soft, reactive metals. Döbereiner also observed that, when arranged by atomic weight, the second member of each triad was roughly the average of the first and the third.[3] This became known as the Law of triads.[citation needed] German chemist Leopold Gmelin worked with this system, and by 1843 he had identified ten triads, three groups of four, and one group of five. Jean Baptiste Dumas published work in 1857 describing relationships between various groups of metals. Although various chemists were able to identify relationships between small groups of elements, they had yet to build one scheme that encompassed them all.[3]

German chemist August Kekulé had observed in 1858 that carbon has a tendency to bond with other elements in a ratio of one to four. Methane, for example, has one carbon atom and four hydrogen atoms. This concept eventually became known as valency. In 1864, fellow German chemist Julius Lothar Meyer published a table of the 49 known elements arranged by valency. The table revealed that elements with similar properties often shared the same valency.[4]

English chemist John Newlands published a series of papers in 1864 and 1865 that described his attempt at classifying the elements: When listed in order of increasing atomic weight, similar physical and chemical properties recurred at intervals of eight, which he likened to the octaves of music.[5][6] This law of octaves, however, was ridiculed by his contemporaries.[7]

Portrait of Dmitri Mendeleev

Russian chemistry professor Dmitri Ivanovich Mendeleev and Julius Lothar Meyer independently published their periodic tables in 1869 and 1870, respectively. They both constructed their tables in a similar manner: by listing the elements in a row or column in order of atomic weight and starting a new row or column when the characteristics of the elements began to repeat.[8] The success of Mendeleev's table came from two decisions he made: The first was to leave gaps in the table when it seemed that the corresponding element had not yet been discovered.[9] Mendeleev was not the first chemist to do so, but he went a step further by using the trends in his periodic table to predict the properties of those missing elements, such as gallium and germanium.[10] The second decision was to occasionally ignore the order suggested by the atomic weights and switch adjacent elements, such as cobalt and nickel, to better classify them into chemical families. With the development of theories of atomic structure, it became apparent that Mendeleev had inadvertently listed the elements in order of increasing atomic number.[11]

With the development of modern quantum mechanical theories of electron configurations within atoms, it became apparent that each row (or period) in the table corresponded to the filling of a quantum shell of electrons. In Mendeleev's original table, each period was the same length. However, because larger atoms have more electron sub-shells, modern tables have progressively longer periods further down the table.[12]

In the years that followed after Mendeleev published his periodic table, the gaps he left were filled as chemists discovered more chemical elements. The last naturally-occurring element to be discovered was Francium (referred to by Mendeleev as eka-caesium) in 1939.[13] The periodic table has also grown with the addition of synthetic and transuranic elements. The first transuranic element to be discovered was neptunium, which was formed by bombarding uranium with neutrons in a cyclotron in 1939.[14]

See also

Notes

  1. ^ Science Standards of Learning Curriculum Framework
  2. ^ Dynamic periodic table
  3. ^ a b Ball, p. 100
  4. ^ Ball, p. 101
  5. ^ Newlands, John A. R. (1864-08-20). "On Relations Among the Equivalents". Chemical News. 10: 94–95.
  6. ^ Newlands, John A. R. (1865-08-18). "On the Law of Octaves". Chemical News. 12: 83.
  7. ^ Bryson, Bill (2004). A Short History of Nearly Everything. London: Black Swan. pp. 141–142. ISBN 9780552151740.
  8. ^ Ball, pp. 100–102
  9. ^ Pullman, p. 227
  10. ^ Ball, p. 105
  11. ^ Atkins, p. 87
  12. ^ Ball, p. 111
  13. ^ Adloff, Jean-Pierre; Kaufman, George B. (2005-09-25). Francium (Atomic Number 87), the Last Discovered Natural Element. The Chemical Educator 10 (5). Retrieved on 2007-03-26.
  14. ^ Ball, p. 123

References

  • Atkins, P. W. (1995). The Periodic Kingdom. HarperCollins Publishers, Inc. ISBN 0-465-07265-8.
  • Ball, Philip (2002). The Ingredients: A Guided Tour of the Elements. Oxford University Press. ISBN 0-19-284100-9.
  • Brown, Theodore L.; LeMay, H. Eugene; Bursten, Bruce E. (2005). Chemistry:The Central Science (10th ed.). Prentice Hall. ISBN 0-13-109686-9.{{cite book}}: CS1 maint: multiple names: authors list (link)
  • Pullman, Bernard (1998). The Atom in the History of Human Thought. Translated by Axel Reisinger. Oxford University Press. ISBN 0-19-515040-6.

Further reading

Template:Unlinkedrefs

  • Bouma, J. (1989). "An Application-Oriented Periodic Table of the Elements". J. Chem. Ed. 66: 741.
  • Eric Scerri (2007). The periodic table: its story and its significance. Oxford [Oxfordshire]: Oxford University Press. ISBN 0-19-530573-6.
  • Imyanitov, N.S. (1999). "Mathematical description of dialectic regular trends in the periodic system". Russ. J. Gen. Chem. 69: 509.
  • Imyanitov, N.S. (2003). "Modification of Various Functions for Description of Periodic Dependences". Russ. J. Coord. Chem. 29: 46. doi:10.1023/A:1021895001562.
  • Mazurs, E.G (1974). Graphical Representations of the Periodic System During One Hundred Years. Alabama: University of Alabama Press.

External links

Template:Link FL