Atomic mass
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The atomic mass (ma or m) is the
The formula used for conversion is:[3][4]
where is the molar mass constant, is the Avogadro constant,[5] and is the experimentally determined molar mass of carbon-12.[6]
The relative isotopic mass (see section below) can be obtained by dividing the atomic mass ma of an isotope by the atomic mass constant mu yielding a
The atomic mass of an isotope and the relative isotopic mass refers to a certain specific isotope of an element. Because substances are usually not isotopically pure, it is convenient to use the elemental atomic mass which is the average (mean) atomic mass of an element, weighted by the abundance of the isotopes. The dimensionless (standard) atomic weight is the weighted mean relative isotopic mass of a (typical naturally occurring) mixture of isotopes.
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 (per E = mc2).
Relative isotopic mass
Relative isotopic mass (a property of a single atom) is not to be confused with the averaged quantity
While atomic mass is an absolute mass, relative isotopic mass is a dimensionless number with no units. This loss of units results from the use of a scaling ratio with respect to a carbon-12 standard, and the word "relative" in the term "relative isotopic mass" refers to this scaling relative to carbon-12.
The relative isotopic mass, then, is the mass of a given isotope (specifically, any single nuclide), when this value is scaled by the mass of carbon-12, where the latter has to be determined experimentally. Equivalently, the relative isotopic mass of an isotope or nuclide is the mass of the isotope relative to 1/12 of the mass of a carbon-12 atom.
For example, the relative isotopic mass of a carbon-12 atom is exactly 12. For comparison, the atomic mass of a carbon-12 atom is exactly 12 daltons. Alternately, the atomic mass of a carbon-12 atom may be expressed in any other mass units: for example, the atomic mass of a carbon-12 atom is 1.99264687992(60)×10−26 kg.
As is the case for the related atomic mass when expressed in daltons, the relative isotopic mass numbers of nuclides other than carbon-12 are not whole numbers, but are always close to whole numbers. This is discussed fully below.
Similar terms for different quantities
The atomic mass or relative isotopic mass are sometimes confused, or incorrectly used, as synonyms of relative atomic mass (also known as atomic weight) or the standard atomic weight (a particular variety of atomic weight, in the sense that it is standardized). However, as noted in the introduction, atomic mass is an absolute mass while all other terms are dimensionless. Relative atomic mass and standard atomic weight represent terms for (abundance-weighted) averages of relative atomic masses in elemental samples, not for single nuclides. As such, relative atomic mass and standard atomic weight often differ numerically from the relative isotopic mass.
The atomic mass (relative isotopic mass) is defined as the mass of a single atom, which can only be one isotope (nuclide) at a time, and is not an abundance-weighted average, as in the case of relative atomic mass/atomic weight. The atomic mass or relative isotopic mass of each isotope and nuclide of a chemical element is, therefore, a number that can in principle be measured to high precision, since every specimen of such a nuclide is expected to be exactly identical to every other specimen, as all atoms of a given type in the same energy state, and every specimen of a particular nuclide, are expected to be exactly identical in mass to every other specimen of that nuclide. For example, every atom of oxygen-16 is expected to have exactly the same atomic mass (relative isotopic mass) as every other atom of oxygen-16.
In the case of many elements that have one naturally occurring isotope (mononuclidic elements) or one dominant isotope, the difference between the atomic mass of the most common isotope, and the (standard) relative atomic mass or (standard) atomic weight can be small or even nil, and does not affect most bulk calculations. However, such an error can exist and even be important when considering individual atoms for elements that are not mononuclidic.
For non-mononuclidic elements that have more than one common isotope, the numerical difference in relative atomic mass (atomic weight) from even the most common relative isotopic mass, can be half a mass unit or more (e.g. see the case of chlorine where atomic weight and standard atomic weight are about 35.45). The atomic mass (relative isotopic mass) of an uncommon isotope can differ from the relative atomic mass, atomic weight, or standard atomic weight, by several mass units.
Relative isotopic masses are always close to whole-number values, but never (except in the case of carbon-12) exactly a whole number, for two reasons:
- protons and neutrons have different masses,[7][8] and different nuclides have different ratios of protons and neutrons.
- atomic masses are reduced, to different extents, by their binding energies.
The ratio of atomic mass to mass number (number of nucleons) varies from 0.9988381346(51) for 56Fe to 1.007825031898(14) for 1H.
Any
Mass defect
![](http://upload.wikimedia.org/wikipedia/commons/thumb/5/53/Binding_energy_curve_-_common_isotopes.svg/300px-Binding_energy_curve_-_common_isotopes.svg.png)
The amount that the ratio of atomic masses to mass number deviates from 1 is as follows: the deviation starts positive at hydrogen-1, then decreases until it reaches a local minimum at helium-4. Isotopes of lithium, beryllium, and boron are less strongly bound than helium, as shown by their increasing mass-to-mass number ratios.
At carbon, the ratio of mass (in daltons) to mass number is defined as 1, and after carbon it becomes less than one until a minimum is reached at iron-56 (with only slightly higher values for iron-58 and nickel-62), then increases to positive values in the heavy isotopes, with increasing atomic number. This corresponds to the fact that nuclear fission in an element heavier than zirconium produces energy, and fission in any element lighter than niobium requires energy. On the other hand, nuclear fusion of two atoms of an element lighter than scandium (except for helium) produces energy, whereas fusion in elements heavier than calcium requires energy. The fusion of two atoms of 4He yielding beryllium-8 would require energy, and the beryllium would quickly fall apart again. 4He can fuse with tritium (3H) or with 3He; these processes occurred during Big Bang nucleosynthesis. The formation of elements with more than seven nucleons requires the fusion of three atoms of 4He in the triple-alpha process, skipping over lithium, beryllium, and boron to produce carbon-12.
Here are some values of the ratio of atomic mass to mass number:[10]
Nuclide | Ratio of atomic mass to mass number |
---|---|
1H | 1.007825031898(14) |
2H | 1.0070508889220(75) |
3H | 1.005349760440(27) |
3He | 1.005343107322(20) |
4He | 1.000650813533(40) |
6Li | 1.00252048124(26) |
12C | 1 |
14N | 1.000219571732(17) |
16O | 0.999682163704(20) |
56Fe | 0.9988381346(51) |
210Po | 0.9999184461(59) |
232Th | 1.0001640242(66) |
238U | 1.0002133905(67) |
Measurement of atomic masses
Direct comparison and measurement of the masses of atoms is achieved with mass spectrometry.
Relationship between atomic and molecular masses
Similar definitions apply to molecules. One can calculate the molecular mass of a compound by adding the atomic masses (not the standard atomic weights) of its constituent atoms. Conversely, the molar mass is usually computed from the standard atomic weights (not the atomic or nuclide masses). Thus, molecular mass and molar mass differ slightly in numerical value and represent different concepts. Molecular mass is the mass of a molecule, which is the sum of its constituent atomic masses. Molar mass is an average of the masses of the constituent molecules in a chemically pure but isotopically heterogeneous ensemble. In both cases, the multiplicity of the atoms (the number of times it occurs) must be taken into account, usually by multiplication of each unique mass by its multiplicity.
Molar mass of CH4 | |||
---|---|---|---|
Standard atomic weight | Number | Total molar mass (g/mol) or molecular weight (Da or g/mol) | |
C | 12.011 | 1 | 12.011 |
H | 1.008 | 4 | 4.032 |
CH4 | 16.043 | ||
Molecular mass of 12C1H4 | |||
Nuclide mass | Number | Total molecular mass (Da or u) | |
12C | 12.00 | 1 | 12.00 |
1H | 1.007825 | 4 | 4.0313 |
CH4 | 16.0313 |
History
The first scientists to determine relative atomic masses were
In the 1860s,
In the 20th century, until the 1960s, chemists and physicists used two different atomic-mass scales. The chemists used an "atomic mass unit" (amu) scale such that the natural mixture of oxygen isotopes had an atomic mass 16, while the physicists assigned the same number 16 to only the atomic mass of the most common oxygen isotope (16O, containing eight protons and eight neutrons). However, because oxygen-17 and oxygen-18 are also present in natural oxygen this led to two different tables of atomic mass. The unified scale based on carbon-12, 12C, met the physicists' need to base the scale on a pure isotope, while being numerically close to the chemists' scale. This was adopted as the 'unified atomic mass unit'. The current International System of Units (SI) primary recommendation for the name of this unit is the dalton and symbol 'Da'. The name 'unified atomic mass unit' and symbol 'u' are recognized names and symbols for the same unit.[12]
The term atomic weight is being phased out slowly and being replaced by relative atomic mass, in most current usage. This shift in nomenclature reaches back to the 1960s and has been the source of much debate in the scientific community, which was triggered by the adoption of the
In 1979, as a compromise, the term "relative atomic mass" was introduced as a secondary synonym for atomic weight. Twenty years later the primacy of these synonyms was reversed, and the term "relative atomic mass" is now the preferred term.
However, the term "standard atomic weights" (referring to the standardized expectation atomic weights of differing samples) has not been changed,[13] because simple replacement of "atomic weight" with "relative atomic mass" would have resulted in the term "standard relative atomic mass."
See also
References
- ^ "DOE Explains...Nuclei". Energy.gov. Retrieved 2023-04-13.
- ISBN 978-92-822-2272-0.
- ^ Peter J. Mohr, Barry N. Taylor (May 20, 2019). "NIST Standard Reference Database 121. Fundamental Physical Constants. atomic mass constant". The NIST reference on constants, Units and Uncertainty. National Institute of Standards and Technology. Retrieved December 10, 2019.
- ^ "Avogadro constant". The NIST Reference on Constants, Units, and Uncertainty. May 2019. Archived from the original on 2000-10-25. Retrieved 24 June 2021.
- ^ "Molar mass of carbon-12". The NIST Reference on Constants, Units, and Uncertainty. May 2019. Archived from the original on 2000-12-06. Retrieved 24 June 2021.
- ^ "Proton mass in u". The NIST Reference on Constants, Units, and Uncertainty. May 2019. Archived from the original on 2000-12-07. Retrieved 24 June 2021.
- ^ "neutron mass in u". The NIST Reference on Constants, Units, and Uncertainty. May 2019. Archived from the original on 2000-12-07. Retrieved 24 June 2021.
- ^ "Neutron-proton mass difference in u". The NIST Reference on Constants, Units, and Uncertainty. May 2019. Archived from the original on 2012-09-05. Retrieved 24 June 2021.
- S2CID 235282522.
- .
- ^ Bureau International des Poids et Mesures (2019): The International System of Units (SI), 9th edition, English version, page 134. Available at the BIPM website.
- S2CID 96317287.