Abundance of the chemical elements

Estimated proportions of matter, dark matter and dark energy in the universe according to 5 year WMAP data. Only the fraction of the mass and energy in the universe labeled "atoms" is composed of chemical elements.

The abundance of a chemical element is a measure of the occurrence of the element relative to all other elements in a given environment. Abundance is measured in one of three ways: by the mass-fraction (the same as weight fraction); by the mole-fraction (fraction of atoms by numerical count, or sometimes fraction of molecules in gases); or by the volume-fraction. Volume-fraction is a common abundance measure in mixed gases such as planetary atmospheres, and is similar in value to molecular mole-fraction for gas mixtures at relatively low densities and pressures, and ideal gas mixtures. Most abundance values in this article are given as mass-fractions.

For example, the abundance of oxygen in pure water can be measured in two ways: the mass fraction is about 89%, because that is the fraction of water's mass which is oxygen. However, the mole-fraction is 33.3333...% because only 1 atom of 3 in water, H2O, is oxygen. As another example, looking at the mass-fraction abundance of hydrogen and helium in both the Universe as a whole and in the atmospheres of gas-giant planets such as Jupiter, it is 74% for hydrogen and 23–25% for helium; while the (atomic) mole-fraction for hydrogen is 92%, and for helium is 8%, in these environments. Changing the given environment to Jupiter's outer atmosphere, where hydrogen is diatomic while helium is not, changes the molecular mole-fraction (fraction of total gas molecules), as well as the fraction of atmosphere by volume, of hydrogen to about 86%, and of helium to 13%.[Note 1]

The abundance of chemical elements in the universe is dominated by the large amounts of hydrogen and helium which were produced in the Big Bang. Remaining elements, making up only about 2% of the universe, were largely produced by supernovae and certain red giant stars. Lithium, beryllium and boron are rare because although they are produced by nuclear fusion, they are then destroyed by other reactions in the stars.[1][2] The elements from carbon to iron are relatively more common in the universe because of the ease of making them in supernova nucleosynthesis. Elements of higher atomic number than iron (element 26) become progressively more rare in the universe, because they increasingly absorb stellar energy in being produced. Elements with even atomic numbers are generally more common than their neighbors in the periodic table, also due to favorable energetics of formation.

The abundance of elements in the Sun and outer planets is similar to that in the universe. Due to solar heating, the elements of Earth and the inner rocky planets of the Solar System have undergone an additional depletion of volatile hydrogen, helium, neon, nitrogen, and carbon (which volatilizes as methane). The crust, mantle, and core of the Earth show evidence of chemical segregation plus some sequestration by density. Lighter silicates of aluminum are found in the crust, with more magnesium silicate in the mantle, while metallic iron and nickel compose the core. The abundance of elements in specialized environments, such as atmospheres, or oceans, or the human body, are primarily a product of chemical interactions with the medium in which they reside.

Abundance of elements in the Universe

Ten most common elements in the Milky Way Galaxy estimated spectroscopically[3]
Z Element Mass fraction in parts per million
1 Hydrogen 739,000 739000
2 Helium 240,000 240000
8 Oxygen 10,400 10400
6 Carbon 4,600 4600
10 Neon 1,340 1340
26 Iron 1,090 1090
7 Nitrogen 960 960
14 Silicon 650 650
12 Magnesium 580 580
16 Sulfur 440 440

The elements – that is, ordinary (baryonic) matter made of protons, neutrons, and electrons, are only a small part of the content of the Universe. Cosmological observations suggest that only 4.6% of the universe's energy (including the mass contributed by energy, E = mc² ↔ m = E / c²) comprises the visible baryonic matter that constitutes stars, planets, and living beings. The rest is made up of dark energy (68%) and dark matter (27%).[4] These are forms of matter and energy believed to exist on the basis of scientific theory and observational deductions, but they have not been directly observed and their nature is not well understood.

Most standard (baryonic) matter is found in stars and interstellar clouds, in the form of atoms or ions (plasma), although it can be found in degenerate forms in extreme astrophysical settings, such as the high densities inside white dwarfs and neutron stars.

Hydrogen is the most abundant element in the Universe; helium is second. However, after this, the rank of abundance does not continue to correspond to the atomic number; oxygen has abundance rank 3, but atomic number 8. All others are substantially less common.

The abundance of the lightest elements is well predicted by the standard cosmological model, since they were mostly produced shortly (i.e., within a few hundred seconds) after the Big Bang, in a process known as Big Bang nucleosynthesis. Heavier elements were mostly produced much later, inside of stars.

Hydrogen and helium are estimated to make up roughly 74% and 24% of all baryonic matter in the universe respectively. Despite comprising only a very small fraction of the universe, the remaining "heavy elements" can greatly influence astronomical phenomena. Only about 2% (by mass) of the Milky Way galaxy's disk is composed of heavy elements.

These other elements are generated by stellar processes.[5][6][7] In astronomy, a "metal" is any element other than hydrogen or helium. This distinction is significant because hydrogen and helium are the only elements that were produced in significant quantities in the Big Bang. Thus, the metallicity of a galaxy or other object is an indication of stellar activity, after the Big Bang.

The following graph (note log scale) shows abundance of elements in our solar system. The table shows the twelve most common elements in our galaxy (estimated spectroscopically), as measured in parts per million, by mass.[3] Nearby galaxies that have evolved along similar lines have a corresponding enrichment of elements heavier than hydrogen and helium. The more distant galaxies are being viewed as they appeared in the past, so their abundances of elements appear closer to the primordial mixture. Since physical laws and processes are uniform throughout the universe, however, it is expected that these galaxies will likewise have evolved similar abundances of elements.

Estimated abundances of the chemical elements in the Solar system. Hydrogen and helium are most common, from the Big Bang. The next three elements (Li, Be, B) are rare because they are poorly synthesized in the Big Bang and also in stars. The two general trends in the remaining stellar-produced elements are: (1) an alternation of abundance in elements as they have even or odd atomic numbers (the Oddo-Harkins rule), and (2) a general decrease in abundance, as elements become heavier. Iron is especially common because it represents the minimum energy nuclide that can be made by fusion of helium in supernovae.

The abundance of elements in the Solar System (see graph) is in keeping with their origin from the Big Bang and nucleosynthesis in a number of progenitor supernova stars. Very abundant hydrogen and helium are products of the Big Bang, while the next three elements are rare since they had little time to form in the Big Bang and are not made in stars (they are, however, produced in small quantities by breakup of heavier elements in interstellar dust, as a result of impact by cosmic rays).

Beginning with carbon, elements have been produced in stars by buildup from alpha particles (helium nuclei), resulting in an alternatingly larger abundance of elements with even atomic numbers (these are also more stable). The effect of odd-numbered chemical elements generally being more rare in the universe was empirically noticed in 1914, and is known as the Oddo-Harkins rule.

Periodic table showing the cosmogenic origin of each element

Cosmogenesis: In general, such elements up to iron are made in large stars in the process of becoming supernovae. Iron-56 is particularly common, since it is the most stable element that can easily be made from alpha particles (being a product of decay of radioactive nickel-56, ultimately made from 14 helium nuclei). Elements heavier than iron are made in energy-absorbing processes in large stars, and their abundance in the universe (and on Earth) generally decreases with increasing atomic number.

Most abundant nuclides in the Solar System[8]
Nuclide A Mass fraction in parts per million Atom fraction in parts per million
Hydrogen-1 1705,700 909,964
Helium-4 4275,200 88,714
Oxygen-16 165,920 477
Carbon-12 123,032 326
Nitrogen-14 141,105 102
Neon-20 201,548 100
Other nuclides: 3,879 149
Silicon-28 28653 30
Magnesium-24 24513 28
Iron-56 561,169 27
Sulfur-32 32396 16
Helium-3 335 15
Hydrogen-2 223 15
Neon-22 22208 12
Magnesium-26 2679 4
Carbon-13 1337 4
Magnesium-25 2569 4
Aluminium-27 2758 3
Argon-36 3677 3
Calcium-40 4060 2
Sodium-23 2333 2
Iron-54 5472 2
Silicon-29 2934 2
Nickel-58 5849 1
Silicon-30 3023 1
Iron-57 5728 1

Elemental abundance and nuclear binding energy

Loose correlations have been observed between estimated elemental abundances in the universe and the nuclear binding energy curve. Roughly speaking, the relative stability of various atomic nuclides has exerted a strong influence on the relative abundance of elements formed in the Big Bang, and during the development of the universe thereafter. [9] See the article about nucleosynthesis for the explanation on how certain nuclear fusion processes in stars (such as carbon burning, etc.) create the elements heavier than hydrogen and helium.

A further observed peculiarity is the jagged alternation between relative abundance and scarcity of adjacent atomic numbers in the elemental abundance curve, and a similar pattern of energy levels in the nuclear binding energy curve. This alternation is caused by the higher relative binding energy (corresponding to relative stability) of even atomic numbers compared to odd atomic numbers, and is explained by the Pauli Exclusion Principle.[10] The semi-empirical mass formula (SEMF), also called Weizsäcker's formula or the Bethe-Weizsäcker mass formula, gives a theoretical explanation of the overall shape of the curve of nuclear binding energy.[11]

Abundance of elements in the Earth

The Earth formed from the same cloud of matter that formed the Sun, but the planets acquired different compositions during the formation and evolution of the solar system. In turn, the natural history of the Earth caused parts of this planet to have differing concentrations of the elements.

The mass of the Earth is approximately 5.98×1024 kg. In bulk, by mass, it is composed mostly of iron (32.1%), oxygen (30.1%), silicon (15.1%), magnesium (13.9%), sulfur (2.9%), nickel (1.8%), calcium (1.5%), and aluminium (1.4%); with the remaining 1.2% consisting of trace amounts of other elements.[12]

The bulk composition of the Earth by elemental-mass is roughly similar to the gross composition of the solar system, with the major differences being that Earth is missing a great deal of the volatile elements hydrogen, helium, neon, and nitrogen, as well as carbon which has been lost as volatile hydrocarbons. The remaining elemental composition is roughly typical of the "rocky" inner planets, which formed in the thermal zone where solar heat drove volatile compounds into space. The Earth retains oxygen as the second-largest component of its mass (and largest atomic-fraction), mainly from this element being retained in silicate minerals which have a very high melting point and low vapor pressure.

Earth's detailed bulk (total) elemental abundance in table form

Note: these are ordered by atom-fraction abundance (right-most column), not mass-abundance.

An estimate[13] of the elemental abundances in the total mass of the Earth. Note that numbers are estimates, and they will vary depending on source and method of estimation. Order of magnitude of data can roughly be relied upon. ppb (atoms) is parts per billion, meaning that is the number of atoms of a given element in every billion atoms in the Earth.

Abundance of elements in Earth's crust

Abundance (atom fraction) of the chemical elements in Earth's upper continental crust as a function of atomic number. The rarest elements in the crust (shown in yellow) are the most dense. These are precious gold and the platinum group metals. They were further rarefied in the crust by being siderophile (iron-loving) elements, in the Goldschmidt classification of elements, and have thus been depleted from the crust by being relocated into the Earth's core. Their abundance in meteoroid materials is relatively higher. Additionally, tellurium and selenium have been depleted from the crust due to formation of volatile hydrides.

The mass-abundance of the nine most abundant elements in the Earth's crust is approximately: oxygen 46%, silicon 28%, aluminum 8.2%, iron 5.6%, calcium 4.2%, sodium 2.5%, magnesium 2.4%, potassium 2.0%, and titanium 0.61%. Other elements occur at less than 0.15%. For a complete list, see abundance of elements in Earth's crust.

The graph at left illustrates the relative atomic-abundance of the chemical elements in Earth's upper continental crust— the part that is relatively accessible for measurements and estimation.

Many of the elements shown in the graph are classified into (partially overlapping) categories:

  1. rock-forming elements (major elements in green field, and minor elements in light green field);
  2. rare earth elements (lanthanides, La-Lu, and Y; labeled in blue);
  3. major industrial metals (global production >~3×107 kg/year; labeled in red);
  4. precious metals (labeled in purple);
  5. the nine rarest "metals" — the six platinum group elements plus Au, Re, and Te (a metalloid) — in the yellow field. These are rare in the crust from being soluble in iron and thus concentrated in the Earth's core.

Note that there are two breaks where the unstable elements technetium (atomic number: 43) and promethium (atomic number: 61) would be. These are both extremely rare, since on Earth they are only produced through the spontaneous fission of very heavy radioactive elements (for example, uranium, thorium, or the trace amounts of plutonium that exist in uranium ores), or by the interaction of certain other elements with cosmic rays. Both of the first two of these elements have been identified spectroscopically in the atmospheres of stars, where they are produced by ongoing nucleosynthetic processes. There are also breaks where the six noble gases would be, since they are not chemically bound in the Earth's crust, and they are only generated by decay chains from radioactive elements and are therefore extremely rare there. The eight naturally occurring very rare, highly radioactive elements (polonium, astatine, francium, radium, actinium, protactinium, neptunium, and plutonium) are not included, since any of these elements that were present at the formation of the Earth have decayed away eons ago, and their quantity today is negligible and is only produced from the radioactive decay of uranium and thorium.

Oxygen and silicon are notably quite common elements in the crust. They have frequently combined with each other to form common silicate minerals.

Rare-earth elements

"Rare" earth elements is a historical misnomer. The persistence of the term reflects unfamiliarity rather than true rarity. The more abundant rare earth elements are similarly concentrated in the crust compared to commonplace industrial metals such as chromium, nickel, copper, zinc, molybdenum, tin, tungsten, or lead. The two least abundant rare earth elements (thulium and lutetium) are nearly 200 times more common than gold. However, in contrast to the ordinary base and precious metals, rare earth elements have very little tendency to become concentrated in exploitable ore deposits. Consequently, most of the world's supply of rare earth elements comes from only a handful of sources. Furthermore, the rare earth metals are all quite chemically similar to each other, and they are thus quite difficult to separate into quantities of the pure elements.

Differences in abundances of individual rare earth elements in the upper continental crust of the Earth represent the superposition of two effects, one nuclear and one geochemical. First, the rare earth elements with even atomic numbers (58Ce, 60Nd, ...) have greater cosmic and terrestrial abundances than the adjacent rare earth elements with odd atomic numbers (57La, 59Pr, ...). Second, the lighter rare earth elements are more incompatible (because they have larger ionic radii) and therefore more strongly concentrated in the continental crust than the heavier rare earth elements. In most rare earth ore deposits, the first four rare earth elements – lanthanum, cerium, praseodymium, and neodymium – constitute 80% to 99% of the total amount of rare earth metal that can be found in the ore.

Earth's mantle elemental abundance

Main article: Mantle (geology)

The mass-abundance of the eight most abundant elements in the Earth's mantle (see main article above) is approximately: oxygen 45%, magnesium 23%, silicon 22%, iron 5.8%, calcium 2.3%, aluminum 2.2%, sodium 0.3%, potassium 0.3%.

The mantle differs in elemental composition from the crust in having a great deal more magnesium and significantly more iron, while having much less aluminum and sodium.

Earth's core elemental abundance

Due to mass segregation, the core of the Earth is believed to be primarily composed of iron (88.8%), with smaller amounts of nickel (5.8%), sulfur (4.5%), and less than 1% trace elements.[12]

Oceanic elemental abundance

Earth's ocean water elemental abundance
Element Proportion (by mass)
Oxygen 85.84% 85.84
Hydrogen 10.82% 10.82
Chlorine 1.94% 1.94
Sodium 1.08% 1.08
Magnesium 0.1292% 0.1292
Sulfur 0.091% 0.091
Calcium 0.04% 0.04
Potassium 0.04% 0.04
Bromine 0.0067% 0.0067
Carbon 0.0028% 0.0028
Boron 0.00043% 0.00043
For a complete list of the abundance of elements in the ocean, see Abundances of the elements (data page) § Sea water.

Atmospheric elemental abundance

The order of elements by volume-fraction (which is approximately molecular mole-fraction) in the atmosphere is nitrogen (78.1%), oxygen (20.9%),[14] argon (0.96%), followed by (in uncertain order) carbon and hydrogen because water vapor and carbon dioxide, which represent most of these two elements in the air, are variable components. Sulfur, phosphorus, and all other elements are present in significantly lower proportions.

According to the abundance curve graph (above right), argon, a significant if not major component of the atmosphere, does not appear in the crust at all. This is because the atmosphere has a far smaller mass than the crust, so argon remaining in the crust contributes little to mass-fraction there, while at the same time buildup of argon in the atmosphere has become large enough to be significant.

Abundances of elements in urban soils

For a complete list of the abundance of elements in urban soils, see Abundances of the elements (data page)#Urban soils.

Reasons for establishing

In the time of life existence, or at least in the time of the existence of human beings, the abundances of chemical elements within the Earth's crust have not been changed dramatically due to migration and concentration processes except the radioactive elements and their decay products and also noble gases. However, significant changes took place in the distribution of chemical elements. But within the biosphere not only the distribution, but also the abundances of elements have changed during the last centuries.

The rate of a number of geochemical changes taking place during the last decades in the biosphere has become catastrophically high. Such changes are often connected with human activities. To study these changes and to make better informed decisions on diminishing their adverse impact on living organisms, and especially on people, it is necessary to estimate the contemporary abundances of chemical elements in geochemical systems susceptible to the highest anthropogenic impact and having a significant effect on the development and existence of living organisms. One of such systems is the soil of urban landscapes. Settlements occupy less than 10% of the land area, but virtually the entire population of the planet lives within them. The main deposing medium in cities is soil, which ecological and geochemical conditions largely determine the life safety of citizens. So that, one of the priority tasks of the environmental geochemistry is to establish the average contents (abundances) of chemical elements in the soils of settlements.

Methods and results

The half-logarithm graph of the abundances of chemical elements in urban soils. (Alekseenko and Alekseenko, 2014) Chemical elements are distributed extremely irregularly in urban soils, what is also typical for the Earth's crust. Nine elements (O, Si, Ca, C, Al, Fe, H, K, N) make the 97.68% of the considering geochemical system (urban soils). These elements and also Zn, Sr, Zr, Ba, and Pb essentially prevail over the trend line. Part of them could be considered as “inherited” from the concentrations in the Earth's crust; another part is explained as a result of intensive technogenic activity in the cities.

The geochemical properties of urban soils from more than 300 cities in Europe, Asia, Africa, Australia, and America were evaluated.[15] In each settlement samples were collected uniformly throughout the territory, covering residential, industrial, recreational and other urban areas. The sampling was carried out directly from the soil surface and specifically traversed pits, ditches and wells from the upper soil horizon. The number of samples in each locality ranged from 30 to 1000. The published data and the materials kindly provided by a number of geochemists were also incorporated into the research. Considering the great importance of the defined contents, quantitative and quantitative emission spectral, gravimetric, X-ray fluorescence, and partly neutron activation analyses were carried out in parallel approximately in the samples. In a volume of 3–5% of the total number of samples, sampling and analyses of the inner and external controls were conducted. Calculation of random errors and systematic errors allowed to consider the sampling and analytical laboratory work as good.

For every city the average concentrations of elements in soils were determined. To avoid the errors related to unequal number of samples, each city was then represented by only one “averaged” sample. The statistical processing of this data allowed to calculate the average concentrations, which can be considered as the abundances of chemical elements in urban soils.

This graph illustrates the relative abundance of the chemical elements in urban soils, irregularly decreasing in proportion with the increasing atomic masses. Therefore, the evolution of organisms in this system occurs in the conditions of light elements' prevalence. It corresponds to the conditions of the evolutional development of the living matter on the Earth. The irregularity of element decreasing may be somewhat connected, as stated above, with the technogenic influence. The Oddo-Harkins rule, which holds that elements with an even atomic number are more common than elements with an odd atomic number, is saved in the urban soils but with some technogenic complications. Among the considered abundances the even-atomic elements make 91.48% of the urban soils mass. As it is in the Earth's crust, elements with the 4-divisible atomic masses of leading isotope (oxygen-16, silicon-28, calcium-40, carbon-12, iron-56) are sharply prevailing in urban soils.

In spite of significant differences between abundances of several elements in urban soils and those values calculated for the Earth's crust, the general patterns of element abundances in urban soils repeat those in the Earth's crust in a great measure. The established abundances of chemical elements in urban soils can be considered as their geochemical (ecological and geochemical) characteristic, reflecting the combined impact of technogenic and natural processes occurring during certain time period (the end of the 20th century–beginning of the 21st century). With the development of science and technology the abundances may gradually change. The rate of these changes is still poorly predictable. The abundances of chemical elements may be used during various ecological and geochemical studies.

Human body elemental abundance

Element Proportion (by mass)
Oxygen 65% 65
Carbon 18% 18
Hydrogen 10% 10
Nitrogen 3% 3
Calcium 1.5% 1.5
Phosphorus 1.2% 1.2
Potassium 0.2% 0.2
Sulfur 0.2% 0.2
Chlorine 0.2% 0.2
Sodium 0.1% 0.1
Magnesium 0.05% 0.05
Iron < 0.05%
Cobalt < 0.05%
Copper < 0.05%
Zinc < 0.05%
Iodine < 0.05%
Selenium < 0.01%

By mass, human cells consist of 65–90% water (H2O), and a significant portion of the remainder is composed of carbon-containing organic molecules. Oxygen therefore contributes a majority of a human body's mass, followed by carbon. Almost 99% of the mass of the human body is made up of six elements: oxygen, carbon, hydrogen, nitrogen, calcium, and phosphorus. The next 0.75% is made up of the next five elements: potassium, sulfur, chlorine, sodium, and magnesium. Only 17 elements are known for certain to be necessary to human life, with one additional element (fluorine) thought to be helpful for tooth enamel strength. A few more trace elements may play some role in the health of mammals. Boron and silicon are notably necessary for plants but have uncertain roles in animals. The elements aluminium and silicon, although very common in the earth's crust, are conspicuously rare in the human body.[16]

Periodic table highlighting nutritional elements[17]

Nutritional elements in the periodic table
H  He
LiBe  B C N O F Ne
NaMg  AlSiP S ClAr
K CaSc TiVCrMnFeCoNiCuZnGaGeAsSeBrKr
RbSrY  ZrNbMoTcRuRhPdAgCdInSnSbTeI Xe
CsBaLa* HfTaW ReOsIrPtAuHgTlPbBiPoAtRn
FrRaAc** RfDbSgBhHsMtDsRgCnNhFlMcLvTsOg
  * CePrNdPmSmEuGdTbDyHoErTmYbLu
  **ThPaU NpPuAmCmBkCfEsFmMdNoLr
  The four organic basic elements
  Quantity elements
  Essential trace elements
  Suggested function from deprivation effects or active metabolic handling, but no clearly-identified biochemical function in humans
  Limited circumstantial evidence for trace benefits or biological action in mammals
  No evidence for biological action in mammals, but essential in some lower organisms.
(In the case of lanthanum, the definition of an essential nutrient as being indispensible and irreplaceable is not completely applicable due to the extreme similarity of the lanthanides. Thus Ce, Pr, and Nd may be substituted for La without ill effects for organisms using La, and the smaller Sm, Eu, and Gd may also be similarly substituted but cause slower growth.)

See also



  1. Vangioni-Flam, Elisabeth; Cassé, Michel (2012). "Cosmic Lithium-Beryllium-Boron Story". In Spite, Monique. Galaxy Evolution: Connecting the Distant Universe with the Local Fossil Record. Springer Science & Business Media. pp. 77–86.
  2. Trimble, Virginia (1996). "The Origin and Evolution of the Chemical Elements". In Malkan, Matthew A.; Zuckerman, Ben. The origin and evolution of the universe. Sudbury, Mass.: Jones and Bartlett Publishers. p. 101. ISBN 0-7637-0030-4.
  3. 1 2 Croswell, Ken (February 1996). Alchemy of the Heavens. Anchor. ISBN 0-385-47214-5.
  4. What is Dark Energy?, Space.com, 1 May 2013
  5. Suess, Hans; Urey, Harold (1956). "Abundances of the Elements". Reviews of Modern Physics. 28: 53. Bibcode:1956RvMP...28...53S. doi:10.1103/RevModPhys.28.53.
  6. Cameron, A.G.W. (1973). "Abundances of the elements in the solar system". Space Science Reviews. 15: 121. Bibcode:1973SSRv...15..121C. doi:10.1007/BF00172440.
  7. Anders, E; Ebihara, M (1982). "Solar-system abundances of the elements". Geochimica et Cosmochimica Acta. 46 (11): 2363. Bibcode:1982GeCoA..46.2363A. doi:10.1016/0016-7037(82)90208-3.
  8. Arnett, David (1996). Supernovae and Nucleosynthesis (First ed.). Princeton, New Jersey: Princeton University Press. ISBN 0-691-01147-8. OCLC 33162440.
  9. Bell, Jerry A.; GenChem Editorial/Writing Team (2005). "Chapter 3: Origin of Atoms". Chemistry: a project of the American Chemical Society. New York [u.a.]: Freeman. pp. 191–193. ISBN 978-0-7167-3126-9. Correlations between abundance and nuclear binding energy [Subsection title]
  10. Bell, Jerry A.; GenChem Editorial/Writing Team (2005). "Chapter 3: Origin of Atoms". Chemistry: a project of the American Chemical Society. New York [u.a.]: Freeman. p. 192. ISBN 978-0-7167-3126-9. The higher abundance of elements with even atomic numbers [Subsection title]
  11. Bailey, David. "Semi-empirical Nuclear Mass Formula". PHY357: Strings & Binding Energy. University of Toronto. Retrieved 2011-03-31.
  12. 1 2 Morgan, J. W.; Anders, E. (1980). "Chemical composition of Earth, Venus, and Mercury". Proceedings of the National Academy of Sciences. 77 (12): 6973–6977. Bibcode:1980PNAS...77.6973M. doi:10.1073/pnas.77.12.6973. PMC 350422Freely accessible. PMID 16592930.
  13. William F McDonough The composition of the Earth. quake.mit.edu
  14. Zimmer, Carl (3 October 2013). "Earth's Oxygen: A Mystery Easy to Take for Granted". The New York Times. Retrieved 3 October 2013.
  15. Vladimir Alekseenko; Alexey Alekseenko (2014). "The abundances of chemical elements in urban soils". Journal of Geochemical Exploration. Elsevier B.V. 147: 245–249. doi:10.1016/j.gexplo.2014.08.003. ISSN 0375-6742.
  16. Table data from Chang, Raymond (2007). Chemistry (Ninth ed.). McGraw-Hill. p. 52. ISBN 0-07-110595-6.
  17. Nielsen, Forrest H. (1998). "Ultratrace minerals.". In Maurice E. Shils; James A. Olsen; Moshe Shine; A. Catharine Ross. Modern nutrition in health and disease. Baltimore: Lippincott Williams & Wilkins,. pp. 283–303. ISBN 978-0683307696.


  1. Below Jupiter's outer atmosphere, volume fractions are significantly different from mole fractions due to high temperatures (ionization and disproportionation) and high density where the Ideal Gas Law is inapplicable.


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