Angstrom

The angstrom[1][2][3][4] (/ˈæŋstrəm/;[3][5][6] ANG-strəm[5]) or ångström (/ˈɒŋstrəm/)[7][1][8][9][10] is a metric unit of length equal to 10−10 m; that is, one ten-billionth (US) of a metre, a hundred-millionth of a centimetre,[11] 0.1 nanometre, or 100 picometres. Its symbol is Å, a letter of the Swedish alphabet. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874).[11]

angstrom
The width of a hydrogen atom is about 1.1 angstroms; the width of a proton (in black) is 1.7×10−5 angstroms.
General information
Unit systemNon-SI metric unit
Unit ofLength
SymbolÅ
Named afterAnders Jonas Ångström
Conversions
1 Å in ...... is equal to ...
   SI Units   10−10 m = 0.1 nm
   CGS Units   10−8 cm
   Imperial units   3.937008×10−9 in
   Planck units   6.187×1024 lP

The angstrom is 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,[12][13] wavelengths of electromagnetic radiation, and dimensions of integrated circuit parts. The atomic (covalent) radii of phosphorus, sulfur, and chlorine are about 1 angstrom, while that of hydrogen is about 0.5 angstroms. Visible light has wavelengths in the range of 4000–7000 Å.

In the late 19th century, spectroscopists adopted 10−10 of a metre as a convenient unit to express the wavelengths of characteristic spectral lines (monochromatic components of the emission spectrum) of chemical elements. However, they soon realized that the definition of the metre at the time, based on a material artifact, was not accurate enough for their work. So, around 1907 they defined their own unit of length, which they called "Ångström", based on the wavelength of a specific spectral line.[11] It was only in 1960, when the metre was redefined in the same way, that the angstrom became again equal to 10−10 metre.

Even though it is a decimal power fraction of the metre, the angstrom was never part of the SI system of units,[14][15] and it has been increasingly replaced by the nanometre or picometre. Up to 2019, it was listed as a compatible unit by both the International Bureau of Weights and Measures (BIPM) and the US National Institute of Standards and Technology (NIST),[9][10] but it is not mentioned in the 9th edition of the official SI document, the "BIPM Brochure" (2019)[14] or in the NIST version of the same.[15]

The 8th edition of the BIPM brochure (2006)[9] and the NIST guide 811 (2008)[10] used the spelling ångström, with Swedish letters; however, this form is rare in English texts. Some popular US dictionaries list only the spelling angstrom.[2][3]

The accepted symbol is "Å", no matter how the unit is spelled.[1][4][3] However, "A" is often used in less formal contexts or typographically limited media.

History

In 1868, Swedish physicist Anders Jonas 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.)[16][17] Ångström's chart and table of wavelengths in the solar spectrum became widely used in solar physics community, which adopted the unit and named it after him. It subsequently spread to the fields of astronomical spectroscopy, atomic spectroscopy, and then to other sciences that deal with atomic-scale structures.

Although intended to correspond to 10−10 metres, that definition was not accurate enough for spectroscopy work. Until 1960 the metre was defined as the distance between two scratches on a bar of platinum-iridium alloy, kept at the BIPM in Paris in a carefully controlled environment. Reliance on that material standard had led to an early error of about one part in 6000 in the tabulated wavelengths. 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 incorrect that Ångström's corrected results were more in error than the uncorrected ones.[18]

In 1892–1895, Albert A. Michelson and Jean-René Benoît, working at the BIPM with specially developed equipment, determined that the length of the international metre standard was equal to 1553163.5 times the wavelength of the red line of the emission spectrum of electrically excited cadmium vapor.[19] In 1907, the International Union for Cooperation in Solar Research (which later became the International Astronomical Union) defined the international angstrom as precisely 1/6438.4696 of the wavelength of that line (in dry air at 15 °C (hydrogen scale) and 760 mmHg under a gravity of 9.8067 m/s2).[20]

This definition was endorsed at the 7th General Conference on Weights and Measures (CGPM) in 1927, but the material definition of the metre was retained until 1960.[21] From 1927 to 1960, the angstrom 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 angstrom to be redefined as being exactly 0.1 nanometres.

Although still widely used in physics and chemistry, the angstrom 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 discouraged its use, and does not even mention it in the 9th edition of the official standard (2019). The angstrom is also not included in the European Union's catalogue of units of measure that may be used within its internal market.[22]

Angstrom star

After the redefinition of the meter in spectroscopic terms, the Angstrom was formally redefined to be 0.1 nanometers. However, there was briefly thought to be a need for a separate unit of comparable size defined directly in terms of spectroscopy. In 1965, J.A. Bearden defined the Angstrom Star (symbol: Å*) as 0.202901 times the wavelength of the tungsten line.[23][24] This auxiliary unit was intended to be accurate to within 5 parts per million of the version derived from the new meter. Within ten years, the unit had been deemed both insufficiently accurate (with accuracies closer to 15 parts per million) and obsolete due to higher precision measuring equipment.[25]

Symbol

For compatibility reasons, Unicode includes the formal symbol U+212B Å ANGSTROM SIGN (HTML entity Å, Å, or Å), which is deprecated.[26] The angstrom sign is normalized into U+00C5 Å LATIN CAPITAL LETTER A WITH RING ABOVE (HTML entity Å, Å, or Å).[27] The Unicode consortium recommends to use the latter.[26]

Before digital typesetting, the angstrom (or angstrom unit) was sometimes written as "A.U." when the Å glyph was unavailable. This use is evident in Bragg's paper on the structure of ice,[28] 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).[29][30][31]

Its symbol is Å, a separate letter of the Swedish alphabet, not a Roman letter with an additional circle added. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874).[11]

See also
  • Orders of magnitude (length) § 100 picometres (for objects on this scale)
  • Conversion of units
  • X unit

References
  1. "angstrom | Definition of angstrom in English by Oxford Dictionaries". 2019-03-06. Archived from the original on 2019-03-06. Retrieved 2024-01-30.
  2. "Definition of ANGSTROM". www.merriam-webster.com. Retrieved 2024-01-30.
  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. Oxford dictionary of English. Oxford [England]; New York: Oxford University Press. 2010. p. 61. ISBN 978-0-19-957112-3. Archived from the original on May 3, 2023.
  8. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Ångström". doi:10.1351/goldbook.N00350
  9. 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 2021-06-04, retrieved 2021-12-16
  10. Ambler Thompson and Barry N. Taylor (2009): "B.8 Factors for Units Listed Alphabetically". NIST Guide to the SI, National Institutes of Standards and Technology. Accessed on 2019-03-02
  11. Entry "angstrom" in the Oxford English Dictionary, 2nd edition (1986). Retrieved on 2021-11-22 from https://www.oed.com/oed2/00008552 Archived 2021-11-22 at the Wayback Machine.
  12. Arturas Vailionis (2015): "Geometry of Crystals" Lecture slides for MatSci162_172, Geometry; Stanford University. archived on 2015-03-19
  13. "ICSD". Archived from the original on 2014-07-30. Retrieved 2015-01-30.
  14. Bureau international des poids et measures (2019): Le système international d'unités, complete brochure, 9th edition.
  15. NIST (2019): Special Publication 330: The International System of Units (SI) 2019 Edition.
  16. 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.
  17. "A Brief (Incomplete) History of Light and Spectra". ChemTeam.
  18. Brand, John C. D. (1995). Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930. CRC Press. p. 47. ISBN 9782884491631.
  19. Michelson, Albert A. (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. Translated by Benoît, Jean-René: 1–85. From p. 85, translated: "... 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 … 1 m = 1553163,5λR ... It follows that the wavelengths of these emissions, always at 15 °C and at 760 mm, are (averages of three determinations): λR = 0,64384722μ" (where [1 μ = 1×10−6 m]"
  20. 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
  21. 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: Bureau International des Poids et Mesures, 1927, pp. 85–88, archived from the original (PDF) on 2018-11-18
  22. 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.
  23. J. A. Bearden. Selection of the W Kα₁ as the X-Ray Wavelength Standard. Physical Review 2nd series, volume 137, no. 2B, pages 455B – B461 (1965).
  24. "CODATA Value: Angstrom star". 2022-02-06.
  25. Curtis, I.; Morgan, I.; Hart, M.; Milne, A.D. (August 1971). "A New Determination of Avogadro's Number". In Langenberg, D. N.; Taylor, B.N. (eds.). Proceedings of the International Congress on Precision Measurement and Fundamental Constants (Report). Vol. 343. National Bureau of Standards. p. 285.
  26. The Unicode Standard 14, Chapter 22.2 Letterlike Symbols, p. 839
  27. The Unicode Consortium (2008): The Unicode Standard, Version 5.0 Chapter "Symbols". ISBN 978-0-321-48091-0
  28. 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.
  29. On the re-definition of the astronomical unit of length (PDF). XXVIII General Assembly of International Astronomical Union. Beijing, China: International Astronomical Union. 31 August 2012. Resolution B2. ... recommends ... 5. that the unique symbol "au" be used for the astronomical unit.
  30. "Monthly Notices of the Royal Astronomical Society: Instructions for Authors". Oxford Journals. Archived from the original on 22 October 2012. Retrieved 20 March 2015. The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc.
  31. "Manuscript Preparation: AJ & ApJ Author Instructions". American Astronomical Society. Archived from the original on 21 February 2016. Retrieved 29 October 2016. Use standard abbreviations for ... natural units (e.g., au, pc, cm).
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