Carbon-12

Carbon-12 (12C) is the more abundant of the two stable isotopes of carbon (Carbon-13 being the other), amounting to 98.93% of the element carbon;[1] its abundance is due to the triple-alpha process by which it is created in stars. Carbon-12 is of particular importance in its use as the standard from which atomic masses of all nuclides are measured, thus, its atomic mass is exactly 12 daltons by definition. Carbon-12 is composed of 6 protons 6 neutrons and 6 electrons.

Carbon-12,  12C
General
Name, symbolCarbon,12C
Neutrons6
Protons6
Nuclide data
Natural abundance98.93%
Parent isotopes12N
12B
Isotope mass12 u
Spin0
Excess energy0± 0 keV
Binding energy92161.753± 0.014 keV
Complete table of nuclides

History

Before 1959 both the IUPAP and IUPAC used oxygen to define the mole; the chemists defining the mole as the number of atoms of oxygen which had mass 16 g, the physicists using a similar definition but with the oxygen-16 isotope only. The two organizations agreed in 1959/60 to define the mole as follows.

The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 gram of carbon 12; its symbol is "mol".

This was adopted by the CIPM (International Committee for Weights and Measures) in 1967, and in 1971 it was adopted by the 14th CGPM (General Conference on Weights and Measures).

In 1961 the isotope carbon-12 was selected to replace oxygen as the standard relative to which the atomic weights of all the other elements are measured.[2]

In 1980 the CIPM clarified the above definition, defining that the carbon-12 atoms are unbound and in their ground state.

Hoyle state

The Hoyle state is an excited, spinless, resonant state of carbon-12. It is produced via the triple-alpha process, and was predicted to exist by Fred Hoyle in 1954.[3] The existence of the 7.7 MeV resonance Hoyle state is essential for the nucleosynthesis of carbon in helium-burning red giant stars, and predicts an amount of carbon production in a stellar environment which matches observations. The existence of the Hoyle state has been confirmed experimentally, but its precise properties are still being investigated.[4] In 2011, an ab initio calculation of the low-lying states of carbon-12 found (in addition to the ground and excited spin-2 state) a resonance with all of the properties of the Hoyle state.[5][6]

Isotopic purification

The isotopes of carbon can be separated in the form of carbon dioxide gas by cascaded chemical exchange reactions with amine carbamate.[7]

See also

References

  1. ^ "Table of Isotopic Masses and Natural Abundances" (PDF). 1999.
  2. ^ "Atomic Weights and the International Committee — A Historical Review". 2004-01-26.
  3. ^ Hoyle, F. (1954). "On Nuclear Reactions Occurring in Very Hot Stars. I. the Synthesis of Elements from Carbon to Nickel". The Astrophysical Journal Supplement Series. 1: 121. Bibcode:1954ApJS....1..121H. doi:10.1086/190005. ISSN 0067-0049.
  4. ^ Chernykh, M.; Feldmeier, H.; Neff, T.; Von Neumann-Cosel, P.; Richter, A. (2007). "Structure of the Hoyle State in C12" (PDF). Physical Review Letters. 98 (3): 032501. Bibcode:2007PhRvL..98c2501C. doi:10.1103/PhysRevLett.98.032501. PMID 17358679.
  5. ^ Epelbaum, E.; Krebs, H.; Lee, D.; Meißner, U.-G. (2011). "Ab Initio Calculation of the Hoyle State" (PDF). Physical Review Letters. 106 (19): 192501. arXiv:1101.2547. Bibcode:2011PhRvL.106s2501E. doi:10.1103/PhysRevLett.106.192501. PMID 21668146.
  6. ^ Hjorth-Jensen, M. (2011). "Viewpoint: The carbon challenge". Physics. 4: 38. Bibcode:2011PhyOJ...4...38H. doi:10.1103/Physics.4.38.
  7. ^ Kenji Takeshita and Masaru Ishidaa (December 2006). "Optimum design of multi-stage isotope separation process by exergy analysis". ECOS 2004 - 17th International Conference on Efficiency, Costs, Optimization, Simulation, and Environmental Impact of Energy on Process Systems. 31 (15): 3097–3107. doi:10.1016/j.energy.2006.04.002.
Lighter:
carbon-11
Carbon-12 is an
isotope of carbon
Heavier:
carbon-13
Decay product of:
boron-12, nitrogen-12
Decay chain
of carbon-12
Decays to:
stable
Art in Dubai

Art in Dubai is an emerging activity in Dubai, United Arab Emirates. New galleries such as Carbon 12 Dubai, art fairs, artists, art patrons and collectors have grown in number.

Atom

An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms. Atoms are extremely small; typical sizes are around 100 picometers (a ten-billionth of a meter, in the short scale).

Atoms are small enough that attempting to predict their behavior using classical physics – as if they were billiard balls, for example – gives noticeably incorrect predictions due to quantum effects. Through the development of physics, atomic models have incorporated quantum principles to better explain and predict this behavior.

Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and typically a similar number of neutrons. Protons and neutrons are called nucleons. More than 99.94% of an atom's mass is in the nucleus. The protons have a positive electric charge, the electrons have a negative electric charge, and the neutrons have no electric charge. If the number of protons and electrons are equal, that atom is electrically neutral. If an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion.

The electrons of an atom are attracted to the protons in an atomic nucleus by this electromagnetic force. The protons and neutrons in the nucleus are attracted to each other by a different force, the nuclear force, which is usually stronger than the electromagnetic force repelling the positively charged protons from one another. Under certain circumstances, the repelling electromagnetic force becomes stronger than the nuclear force, and nucleons can be ejected from the nucleus, leaving behind a different element: nuclear decay resulting in nuclear transmutation.

The number of protons in the nucleus defines to what chemical element the atom belongs: for example, all copper atoms contain 29 protons. The number of neutrons defines the isotope of the element. The number of electrons influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form chemical compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the physical changes observed in nature and is the subject of the discipline of chemistry.

Atomic mass

The atomic mass (ma) is the mass of an atom. Its unit is the unified atomic mass units (abbr. u) where 1 unified atomic mass unit is defined as ​1⁄12 of the mass of a single carbon-12 atom, at rest. For atoms, the protons and neutrons of the nucleus account for nearly all of the total mass, and the atomic mass measured in u has nearly the same value as the mass number.

When divided by unified atomic mass units, or daltons (abbr. Da), to form a pure numeric ratio, the atomic mass of an atom becomes a dimensionless value called the relative isotopic mass (see section below). Thus, the atomic mass of a carbon-12 atom is 12 u (or 12 Da), but the relative isotopic mass of a carbon-12 atom is simply 12.

The atomic mass or relative isotopic mass refers to the mass of a single particle, and therefore is tied to a certain specific isotope of an element. The dimensionless standard atomic weight instead refers to the average (mathematical mean) of atomic mass values of a typical naturally-occurring mixture of isotopes for a sample of an element. Atomic mass values are thus commonly reported to many more significant figures than atomic weights. Standard atomic weight is related to atomic mass by the abundance ranking of isotopes for each element. It is usually about the same value as the atomic mass of the most abundant isotope, other than what looks like (but is not actually) a rounding difference.

The atomic mass of atoms, ions, or atomic nuclei is slightly less than the sum of the masses of their constituent protons, neutrons, and electrons, due to binding energy mass loss (as per E = mc2).

Atomic mass unit

The unified atomic mass unit or dalton (symbol: u, or Da or AMU) is a standard unit of mass that quantifies mass on an atomic or molecular scale (atomic mass). One unified atomic mass unit is approximately the mass of one nucleon (either a single proton or neutron) and is numerically equivalent to 1 g/mol. It is defined as one twelfth of the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest, and has a value of 1.660539040(20)×10−27 kg, or approximately 1.66 yoctograms. The CIPM has categorised it as a non-SI unit accepted for use with the SI, and whose value in SI units must be obtained experimentally.The atomic mass unit (amu) without the "unified" prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, many sources still use the term amu but now define it in the same way as u (i.e., based on carbon-12). In this sense, most uses of the terms atomic mass units and amu, today, actually refer to unified atomic mass unit. For standardization, a specific atomic nucleus (carbon-12 vs. oxygen-16) had to be chosen because the average mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than (and not equal to) 1 u.

The atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass (me).

Until the 2019 redefinition of SI base units, the number of daltons in a gram is exactly the Avogadro number by definition, or equivalently, a dalton is exactly equivalent to 1 gram/mol. Thereafter, these relationships will no longer be exact, but they will still be extremely accurate approximations.

Avogadro constant

The Avogadro constant, named after scientist Amedeo Avogadro, is the number of constituent particles, usually molecules, atoms or ions that are contained in the amount of substance given by one mole. It is the proportionality factor that relates the molar mass of a substance to the mass of a sample, is designated with the symbol NA or L, and has the value 6.022140857(74)×1023 mol−1 in the International System of Units (SI).Previous definitions of chemical quantity involved the Avogadro number, a historical term closely related to the Avogadro constant, but defined differently: the Avogadro number was initially defined by Jean Baptiste Perrin as the number of atoms in one gram-molecule of atomic hydrogen, meaning one gram of hydrogen. This number is also known as Loschmidt constant in German literature. The constant was later redefined as the number of atoms in 12 grams of the isotope carbon-12 (12C), and still later generalized to relate amounts of a substance to their molecular weight. For instance, the number of nucleons (protons and neutrons) in one mole of any sample of ordinary matter is, to a first approximation, 6×1023 times its molecular weight. Similarly, 12 grams of 12C, with the mass number 12 (6 protons, 6 neutrons), has a similar number of carbon atoms, 6.022×1023. The Avogadro number is a dimensionless quantity, and has the same numerical value of the Avogadro constant when given in base units. In contrast, the Avogadro constant has the dimension of reciprocal amount of substance. The Avogadro constant can also be expressed as 0.6023... mL⋅mol−1⋅Å−3, which can be used to convert from volume per molecule in cubic ångströms to molar volume in millilitres per mole.

Pending revisions in the base set of SI units necessitated redefinitions of the concepts of chemical quantity. The Avogadro number, and its definition, was deprecated in favor of the Avogadro constant and its definition. Based on measurements made through the middle of 2017 which calculated a value for the Avogadro constant of NA = 6.022140758(62)×1023 mol−1, the redefinition of SI units is planned to take effect on 20 May 2019. The value of the constant will be fixed to exactly 6.02214076×1023 mol−1.

CNO cycle

The CNO cycle (for carbon–nitrogen–oxygen) is one of the two known sets of fusion reactions by which stars convert hydrogen to helium, the other being the proton–proton chain reaction (pp-chain reaction). Unlike the latter, the CNO cycle is a catalytic cycle. It is dominant in stars that are more than 1.3 times as massive as the Sun.In the CNO cycle, four protons fuse, using carbon, nitrogen, and oxygen isotopes as catalysts, to produce one alpha particle, two positrons and two electron neutrinos. Although there are various paths and catalysts involved in the CNO cycles, all these cycles have the same net result:

4 11H + 2 e− → 42He + 2 e+ + 2 e− + 2 νe + 3 γ + 24.7 MeV → 42He + 2 νe + 3 γ + 26.7 MeVThe positrons will almost instantly annihilate with electrons, releasing energy in the form of gamma rays. The neutrinos escape from the star carrying away some energy. One nucleus goes on to become carbon, nitrogen, and oxygen isotopes through a number of transformations in an endless loop.

The proton–proton chain is more prominent in stars the mass of the Sun or less. This difference stems from temperature dependency differences between the two reactions; pp-chain reaction starts at temperatures around 4×106 K (4 megakelvin), making it the dominant energy source in smaller stars. A self-maintaining CNO chain starts at approximately 15×106 K, but its energy output rises much more rapidly with increasing temperatures so that it becomes the dominant source of energy at approximately 17×106 K.

The Sun has a core temperature of around 15.7×106 K, and only 1.7% of 4He nuclei produced in the Sun are

born in the CNO cycle. The CNO-I process was independently proposed by Carl von Weizsäcker and Hans Bethe in the late 1930s.

Carbon-13

Carbon-13 (13C) is a natural, stable isotope of carbon with a nucleus containing six protons and seven neutrons. As one of the environmental isotopes, it makes up about 1.1% of all natural carbon on Earth.

Carbon-14

Carbon-14, (14C), or radiocarbon, is a radioactive isotope of carbon with an atomic nucleus containing 6 protons and 8 neutrons. Its presence in organic materials is the basis of the radiocarbon dating method pioneered by Willard Libby and colleagues (1949) to date archaeological, geological and hydrogeological samples. Carbon-14 was discovered on February 27, 1940, by Martin Kamen and Sam Ruben at the University of California Radiation Laboratory in Berkeley, California. Its existence had been suggested by Franz Kurie in 1934.There are three naturally occurring isotopes of carbon on Earth: carbon-12, which makes up 99% of all carbon on Earth; carbon-13, which makes up 1%; and carbon-14, which occurs in trace amounts, making up about 1 or 1.5 atoms per 1012 atoms of carbon in the atmosphere. Carbon-12 and carbon-13 are both stable, while carbon-14 is unstable and has a half-life of 5,730±40 years. Carbon-14 decays into nitrogen-14 through beta decay. A gram of carbon containing 1 atom of carbon-14 per 1012 atoms will emit ~0.2 beta particles per second. The primary natural source of carbon-14 on Earth is cosmic ray action on nitrogen in the atmosphere, and it is therefore a cosmogenic nuclide. However, open-air nuclear testing between 1955–1980 contributed to this pool.

The different isotopes of carbon do not differ appreciably in their chemical properties. This resemblance is used in chemical and biological research, in a technique called carbon labeling: carbon-14 atoms can be used to replace nonradioactive carbon, in order to trace chemical and biochemical reactions involving carbon atoms from any given organic compound.

Isotope

Isotopes are variants of a particular chemical element which differ in neutron number, and consequently in nucleon number. All isotopes of a given element have the same number of protons but different numbers of neutrons in each atom.The term isotope is formed from the Greek roots isos (ἴσος "equal") and topos (τόπος "place"), meaning "the same place"; thus, the meaning behind the name is that different isotopes of a single element occupy the same position on the periodic table. It was coined by a Scottish doctor and writer Margaret Todd in 1913 in a suggestion to chemist Frederick Soddy.

The number of protons within the atom's nucleus is called atomic number and is equal to the number of electrons in the neutral (non-ionized) atom. Each atomic number identifies a specific element, but not the isotope; an atom of a given element may have a wide range in its number of neutrons. The number of nucleons (both protons and neutrons) in the nucleus is the atom's mass number, and each isotope of a given element has a different mass number.

For example, carbon-12, carbon-13 and carbon-14 are three isotopes of the element carbon with mass numbers 12, 13 and 14 respectively. The atomic number of carbon is 6, which means that every carbon atom has 6 protons, so that the neutron numbers of these isotopes are 6, 7 and 8 respectively.

Isotopes of carbon

Carbon (6C) has 15 known isotopes, from 8C to 22C, of which 12C and 13C are stable. The longest-lived radioisotope is 14C, with a half-life of 5,700 years. This is also the only carbon radioisotope found in nature—trace quantities are formed cosmogenically by the reaction 14N + 1n → 14C + 1H. The most stable artificial radioisotope is 11C, which has a half-life of 20.334 minutes. All other radioisotopes have half-lives under 20 seconds, most less than 200 milliseconds. The least stable isotope is 8C, with a half-life of 2.0 x 10−21 s.

Isotopes of sulfur

Sulfur (16S) has 24 known isotopes with mass numbers ranging from 26 to 49, four of which are stable: 32S (95.02%), 33S (0.75%), 34S (4.21%), and 36S (0.02%). The preponderance of sulfur-32 is explained by its production from carbon-12 plus successive fusion capture of five helium nuclei, in the so-called alpha process of exploding type II supernovas (see silicon burning).

Other than 35S, the radioactive isotopes of sulfur are all comparatively short-lived. 35S is formed from cosmic ray spallation of 40Ar in the atmosphere. It has a half-life of 87 days. The next longest-lived radioisotope is sulfur-38, with a half-life of 17 minutes. The shortest-lived is 49S, with a half-life shorter than 200 nanoseconds.

When sulfide minerals are precipitated, isotopic equilibration among solids and liquid may cause small differences in the δS-34 values of co-genetic minerals. The differences between minerals can be used to estimate the temperature of equilibration. The δC-13 and δS-34 of coexisting carbonates and sulfides can be used to determine the pH and oxygen fugacity of the ore-bearing fluid during ore formation.

In most forest ecosystems, sulfate is derived mostly from the atmosphere; weathering of ore minerals and evaporites also contribute some sulfur. Sulfur with a distinctive isotopic composition has been used to identify pollution sources, and enriched sulfur has been added as a tracer in hydrologic studies. Differences in the natural abundances can also be used in systems where there is sufficient variation in the 34S of ecosystem components. Rocky Mountain lakes thought to be dominated by atmospheric sources of sulfate have been found to have different δS-34 values from oceans believed to be dominated by watershed sources of sulfate.

Kilogram

The kilogram or kilogramme (symbol: kg) is the base unit of mass in the International System of Units (SI). Until 20 May 2019, it remains defined by a platinum alloy cylinder, the International Prototype Kilogram (informally Le Grand K or IPK), manufactured in 1889, and carefully stored in Saint-Cloud, a suburb of Paris. After 20 May, it will be defined in terms of fundamental physical constants.

The kilogram was originally defined as the mass of a litre (cubic decimetre) of water. That was an inconvenient quantity to precisely replicate, so in 1799 a platinum artefact was fashioned to define the kilogram. That artefact, and the later IPK, have been the standard of the unit of mass for the metric system ever since.

In spite of best efforts to maintain it, the IPK has diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to efforts to develop measurement technology precise enough to allow replacing the kilogram artifact with a definition based directly on physical phenomena, a process which is scheduled to finally take place in 2019.

The new definition is based on invariant constants of nature, in particular the Planck constant which will change to being defined rather than measured, thereby fixing the value of the kilogram in terms of the second and the metre, and eliminating the need for the IPK. The new definition was approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018. The Planck constant relates a light particle’s energy, and hence mass, to its frequency. The new definition only became possible when instruments were devised to measure the Planck constant with sufficient accuracy based on the IPK definition of the kilogram.

List of museums in the United Arab Emirates

This is a list of museums in the United Arab Emirates.

Al Ahmadiya School

Al Ain National Museum

Al Eslah School Museum

Al Hisn Fort Museum

Dubai Museum

Etihad Museum

Fujairah Heritage Village

Fujairah Museum

Guggenheim Abu Dhabi

Louvre Abu Dhabi

Saeed Al Maktoum House

Salsali Private Museum

Salwa Zeidan Gallery

Sharjah Art Museum

Sharjah Museum of Islamic Civilization

Sharjah Maritime Museum

Sharjah Heritage Museum

Sharjah Classic Cars Museum

Sharjah Calligraphy Museum

Sharjah Archaeology Museum

Sheikh Obaid bin Thani House

Sheikh Zayed Palace Museum

Zayed National Museum

Tanki Online Museum

Carbon 12 Dubai

Mass excess

The mass excess of a nuclide is the difference between its actual mass and its mass number in atomic mass units. It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference for most nuclides) by its mass number, which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons. Thus, the mass excess is an expression of the nuclear binding energy, relative to the binding energy per nucleon of carbon-12 (which defines the atomic mass unit). If the mass excess is negative, the nucleus has more binding energy than 12C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it can radioactively decay, releasing energy.

Mass number

The mass number (symbol A, from the German word Atomgewicht (atomic weight), also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It determines the atomic mass of atoms. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion. The mass number is different for each different isotope of a chemical element. This is not the same as the atomic number (Z) which denotes the number of protons in a nucleus, and thus uniquely identifies an element. Hence, the difference between the mass number and the atomic number gives the number of neutrons (N) in a given nucleus: .

The mass number is written either after the element name or as a superscript to the left of an element's symbol. For example, the most common isotope of carbon is carbon-12, or 12
C
, which has 6 protons and 6 neutrons. The full isotope symbol would also have the atomic number (Z) as a subscript to the left of the element symbol directly below the mass number: 12
6
C
. This is technically redundant, as each element is defined by its atomic number, so it is often omitted.

Molar mass constant

The molar mass constant, symbol Mu, is a physical constant which relates relative atomic mass and molar mass. Its value is defined to be 1 g/mol in SI units.

The molar mass constant is important in writing dimensionally correct equations. It is common to see phrases such as

The molar mass of an element is the atomic weight in grams per mole.

However, atomic weight, i.e., relative atomic mass, is a dimensionless quantity, and cannot take the units of grams per mole. Formally, the operation is the multiplication by a constant which has the value 1 g/mol, that is the molar mass constant.

The molar mass constant is unusual (but not unique) among physical constants by having an exactly defined value rather than being measured experimentally. It is fixed by the definitions of the mole and of relative atomic mass. From the definition of the mole, the molar mass of carbon 12 is exactly 12 g/mol. From the definition of relative atomic mass, the relative atomic mass of carbon 12, that is the atomic weight of a sample of pure carbon 12, is exactly 12. The molar mass constant is given by

The speed of light, the electric constant and the magnetic constant are other examples of physical constants whose values are fixed by the definitions of the International System of Units (SI), in these cases by the definitions of the metre and the ampere.

The molar mass constant is also related to the mass of a carbon-12 atom in grams:

Hence the uncertainty in the value of the mass of a carbon-12 atom in SI units is governed by the uncertainty in the Avogadro constant: the CODATA 2006 recommended value is 1.992 646 54(10)×10−26 kg (ur = 5×10−8).

The relatively simple value of the molar mass constant in SI units is also a consequence of the way in which the International System of Units is defined. It is possible to quote the value of the molar mass constant in other units: for example, it is equal to (1/453.592 37) lb/mol ~ 2.204 623 262 × 10−3 lb/mol.

Mole (unit)

The mole is the base unit of amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly 6.02214076×1023 (Avogadro constant) constitutive particles, e.g., atoms, molecules, ions or electrons.This definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (12C) (the isotope of carbon with relative atomic mass 12 Da by definition). The mole is an SI base unit, with the unit symbol mol.

The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (mol/l), commonly abbreviated M.

The term gram-molecule was formerly used for essentially the same concept. The term gram-atom has been used for a related but distinct concept, namely a quantity of a substance that contains an Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.

Relative atomic mass

Relative atomic mass (symbol: Ar) or atomic weight is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to one unified atomic mass unit. The unified atomic mass unit (symbol: u or Da) is defined as being ​1⁄12 of the atomic mass of a carbon-12 atom. Since both values in the ratio are expressed in the same unit (u), the resulting value is dimensionless; hence the value is said to be relative.

For a single given sample, the relative atomic mass of a given element is the weighted arithmetic mean of the masses of the individual atoms (including their isotopes) that are present in the sample. This quantity can vary substantially between samples because the sample's origin (and therefore its radioactive history or diffusion history) may have produced unique combinations of isotopic abundances. For example, due to a different mixture of stable carbon-12 and carbon-13 isotopes, a sample of elemental carbon from volcanic methane will have a different relative atomic mass than one collected from plant or animal tissues.

The more common, and more specific quantity known as standard atomic weight (Ar, standard) is an application of the relative atomic mass values obtained from multiple different samples. It is sometimes interpreted as the expected range of the relative atomic mass values for the atoms of a given element from all terrestrial sources, with the various sources being taken from Earth. "Atomic weight" is often loosely and incorrectly used as a synonym for standard atomic weight (incorrectly because standard atomic weights are not from a single sample). Standard atomic weight is nevertheless the most widely published variant of relative atomic mass.

Additionally, the continued use of the term "atomic weight" (for any element) as opposed to "relative atomic mass" has attracted considerable controversy since at least the 1960s, mainly due to the technical difference between weight and mass in physics. Still, both terms are officially sanctioned by the IUPAC. The term "relative atomic mass" now seems to be replacing "atomic weight" as the preferred term, although the term "standard atomic weight" (as opposed to the more correct "standard relative atomic mass") continues to be used.

Triple-alpha process

The triple-alpha process is a set of nuclear fusion reactions by which three helium-4 nuclei (alpha particles) are transformed into carbon.

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