Angstrom

The angstrom[1][2][3][4] (/ˈæŋstrəm/, /ˈæŋstrʌm/;[3][5][6] ANG-strəm, ANG-strum[5]) or ångström[1][7][8][9] is a metric unit of length equal to 10−10 m; that is, one ten-billionth of a metre, 0.1 nanometre, or 100 picometres. Its symbol is Å, a letter of the Swedish alphabet.

Ångström
Anders Jonas Ångström, after whom the unit was named.
General information
Unit ofLength
SymbolÅ 
Named afterAnders Jonas Ångström
Conversions
1 Å in ...... is equal to ...
   metres   10−10 m
   centimetres   10−8 cm
   micrometres   10−4 μm
   nanometres   0.1 nm
   picometres   100 pm

The ångström is not a part of the SI system of units, but it can be considered part of the metric system in general.[8][9] Although deprecated by both the International Bureau of Weights and Measures (BIPM) and the US National Institute of Standards and Technology (NIST), the unit is still often used in the natural sciences and technology to express sizes of atoms, molecules, microscopic biological structures, and lengths of chemical bonds, arrangement of atoms in crystals, wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. The atomic (covalent) radii of phosphorus, sulfur, and chlorine are about 1 ångström, while that of hydrogen is about 0.5 ångströms. Visible light has wavelengths in the range of 4000–7000 Å.

The unit is named after 19th-century Swedish physicist Anders Jonas Ångström (Swedish: [ˈɔ̂ŋːstrœm]). The BIPM and NIST use the spelling ångström, including Swedish letters;[8][9] but this form is rare in English texts. Some popular US dictionaries list only the spelling angstrom.[2][3] The symbol should always be "Å", no matter how the unit is spelled.[1][4][3] Nonetheless, "A" is often used in less formal contexts or typographically limited media.

Use

The ångström is used extensively in crystallography, solid-state physics and chemistry as a unit for d-spacings (the distance between atomic planes in a crystal[10]), cell parameters, inter-atomic distances and x-ray wavelengths, as these values are often in the 1–10 Å range. For example, the Inorganic Crystal Structure Database[11] presents all these values using the ångström.

History

Anders Jonas Ångström was a pioneer in the field of spectroscopy, and he is also well known for his studies of astrophysics, heat transfer, terrestrial magnetism, and the aurora borealis. In 1852, Ångström formulated in Optiska undersökningar (Optical researches),[12] a law of absorption, later modified somewhat and known as Kirchhoff's law of thermal radiation.

In 1868, Ångström created a chart of the spectrum of sunlight, in which he expressed the wavelengths of electromagnetic radiation in the electromagnetic spectrum in multiples of one ten-millionth of a millimetre (or 10−7 mm.)[13][14] Because the human eye is sensitive to wavelengths from about 4000 to 7000 Å (visible light), that choice of unit supported sufficiently accurate measurements of visible wavelengths without resorting to fractional numbers. Ångström's chart and table of wavelengths in the solar spectrum became widely used in solar physics, which adopted the unit and named it after him. It subsequently spread to the rest of astronomical spectroscopy, atomic spectroscopy, and subsequently to other sciences that deal with atomic-scale structures.

Although intended to correspond to 10−10 metres, for precise spectral analysis, the ångström had to be defined more accurately than the metre, which until 1960 was still defined based on the length of a bar of metal held in Paris. The use of metal bars had been involved in an early error in the value of the ångström of about one part in 6000. Ångström took the precaution of having the standard bar he used checked against a standard in Paris, but the metrologist Henri Tresca reported it to be so much shorter than it really was that Ångström's corrected results were more in error than the uncorrected ones.[15]

Example about how the theoretical atomic radii calculated in Ångströms are plotted as a function of the atomic number.

In 1892–1895, Albert A. Michelson defined the ångström so that the red line of cadmium was equal to 6438.47 ångströms.[16] In 1907, the International Union for Cooperation in Solar Research (which later became the International Astronomical Union) defined the international ångström by declaring the wavelength of the red line of cadmium (in dry air at 15 °C (hydrogen scale) and 760 mmHg under a gravity of 9.8067 m/s2) equal to 6438.4696 international ångströms, and this definition was endorsed by the International Bureau of Weights and Measures in 1927.[17][18] From 1927 to 1960, the ångström remained a secondary unit of length for use in spectroscopy, defined separately from the metre. In 1960, the metre itself was redefined in spectroscopic terms, which allowed the ångström to be redefined as being exactly 0.1 nanometres.

The ångström is internationally recognized, but is not a formal part of the International System of Units (SI). The closest SI unit is the nanometre (10−9 m). The International Committee for Weights and Measures officially discourages its use, and it is not included in the European Union's catalogue of units of measure that may be used within its internal market.[19]

Symbol
Example of the Unicode codification.

For compatibility reasons, Unicode includes the formal symbol at U+212B Å ANGSTROM SIGN (HTML Å). However, the ångström sign is also normalized into U+00C5 Å LATIN CAPITAL LETTER A WITH RING ABOVE (HTML Å · Å, Å)[20] The Unicode consortium recommends to use the regular letter (00C5).

Before digital typesetting, the ångström (or ångström unit) was sometimes written as "A.U.". This use is evident in Bragg's paper on the structure of ice,[21] which gives the c- and a-axis lattice constants as 4.52 A.U. and 7.34 A.U., respectively. Ambiguously, the abbreviation "a.u." may also refer to the atomic unit of length, the bohr—about 0.53 Å—or the much larger astronomical unit (about 1.5×1011 m).

gollark: I figure it's not hugely useful linking to all the many, many individual function documentation pages. So maybe only the important functions, important *APIs*, or more freeform documentation for other stuff.
gollark: A link to the main page is useful, Yemmel's project idea list, maybe other things?
gollark: The CC:T wiki?
gollark: That is an oddly specific scenario. And you can just check the online version *now*.
gollark: I check Wikipedia rather than using the (surprisingly small) database dump, partly because the database dump is text-only and the software for viewing it is lacking, and partly because there's just no particular reason to not use the online one.

See also

References
  1. Entry "angstrom" in the Oxford online dictionary. Retrieved on 2019-03-02 from https://en.oxforddictionaries.com/definition/angstrom.
  2. Entry "angstrom" in the Merriam-Webster online dictionary. Retrieved on 2019-03-02 from https://www.merriam-webster.com/dictionary/angstrom.
  3. "Angstrom". Collins English Dictionary. Retrieved 2019-03-02.
  4. Webster's Encyclopedic Unabridged Dictionary of the English Language. Portland House, 1989
  5. Wells, John C. (2008), Longman Pronunciation Dictionary (3rd ed.), Longman, ISBN 9781405881180
  6. Roach, Peter (2011), Cambridge English Pronouncing Dictionary (18th ed.), Cambridge: Cambridge University Press, ISBN 9780521152532
  7. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Ångström". doi:10.1351/goldbook.N00350
  8. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 127, ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14
  9. Ambler Thompson and Barry N. Taylor (2010): "B.8 Factors for Units Listed Alphabetically". NIST Guide to the SI, National Institutes of Standards and Technology. Accessed on 2019-03-02
  10. Vailionis, Arturas. "Geometry of Crystals" (PDF). Archived from the original (PDF) on 2015-03-19. Retrieved 2015-04-20.
  11. "ICSD". Archived from the original on 2014-07-30. Retrieved 2015-01-30.
  12. See:
    • Ångström, A.J. (1852). "Optiska undersökningar" [Optical investigations]. Kongliga Vetenskaps-Akademiens Handlingar [Proceedings of the Royal Academy of Science] (in Swedish). 40: 333–360. Note: Although Ångström submitted his paper to the Swedish Royal Academy of Science on 16 February 1853, it was published in the volume for Academy's proceedings of 1852.
    • German translation: Ångström, A.J. (1855). "Optische Untersuchungen" [Optical investigations]. Annalen der Physik und Chemie (in German). 94: 141–165.
    • English translation: Ångström, A.J. (1855). "Optical researches". Philosophical Magazine. 4th series. 9: 327–342.
  13. Ångström, A.J. (1868). Recherches sur le spectre solaire [Investigations of the solar spectrum] (in French). Uppsala, Sweden: W. Schultz. The 1869 edition (printed by Ferdinand Dümmler in Berlin) contains sketches of the solar spectrum.
  14. "A Brief (Incomplete) History of Light and Spectra". ChemTeam.
  15. Brand, John C. D. (1995). Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930. CRC Press. p. 47. ISBN 9782884491631.
  16. Michelson, Albert A.; Benoît, Jean-René, tr. (1895). "Détermination expérimentale de la valeur du mètre en longueurs d'ondes lumineuses" [Experimental determination of the value of the meter in terms of the lengths of light waves]. Travaux et Mémoires du Bureau International des Poids et Mesures (in French). 11: 1–85. From p. 85: " … la conclusion finale de ce travail est que l'unité fondamentale du Systéme métrique est représentée par les nombres suivants de longuers d'onde des trois radiations du cadmium, dans l'air à 15°C. (') et sous la pression de 760 mm: Radiations rouges … 1m = 1 553 163,5 λ R … Il en résulte que les longueurs d'onde de ces radiations, toujours à 15° et sous 760 mm, sont (moyennes des trois déterminations): λR = 0,643 847 22 μ, … " ( … the final conclusion of this work is that the fundamental unit of the metric system is represented by the following numbers of wavelengths of three emissions of cadmium, in air at 15°C and at a pressure of 760 mm: Red emission … 1m = 1 553 163,5 λR … It follows that the wavelengths of these emissions, always at 15°C and at 760 mm, are (averages of three determinations): λR = 0,643 847 22 μ, … [1μ = 1×10–6m])
  17. Benoît, Jean-René; Fabry, Charles; and Pérot, Alfred; « Nouvelle Détermination du mètre en longueurs d'ondes lumineuses » ["A New Determination of the Metre in Terms of the Wave-length of Light"], Comptes rendus hebdomadaires des séances de l'Académie des sciences, vol. 144, 21 May 1907, p. 1082-1086
  18. Comptes rendus de la 7e réunion de la Conférence générale des poids et mesures [Proceedings of the 7th meeting of the General conference of weights and measures] (PDF) (in French), Paris, 1927, pp. 85–88
  19. The Council of the European Communities (27 May 2009). "Council Directive 80/181/EEC of 20 December 1979 on the approximation of the laws of the Member States relating to Unit of measurement and on the repeal of Directive 71/354/EEC". Retrieved 2011-09-23.
  20. The Unicode Consortium (2007). "Symbols" (PDF). The Unicode Standard, Version 5.0. Addison-Wesley. p. 493. ISBN 978-0-321-48091-0. OCLC 145867322..
  21. Bragg, William H. (1921). "The Crystal Structure of Ice". Proceedings of the Physical Society of London. 34 (1): 98. Bibcode:1921PPSL...34...98B. doi:10.1088/1478-7814/34/1/322.

Bibliography
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