Ångström

For other uses, see Ångström (disambiguation).
Ångström
Unit of Length
Symbol Å 
Named after Anders Jonas Ångström
Unit 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
Anders Jonas Ångström.

The ångström (Swedish: [ˈɔŋstrøm]) or angstrom is a unit of length equal to 10−10 m (one ten-billionth of a metre) or 0.1 nm. Its symbol is Å, a letter in the Swedish alphabet.

The natural sciences and technology often use ångström 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. Atoms of phosphorus, sulfur, and chlorine are about an ångström in covalent radius, while a hydrogen atom is about half an ångström; see atomic radius.

The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874). The symbol is always written with a ring diacritic, as the letter in the Swedish alphabet. The unit's name is often written in English without the diacritics,[1] but the official definitions contain diacritics.[2][3]

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[4]), 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[5] presents all these values using the ångström.

History

Anders Jonas Ångström was a pioneer in the field of spectroscopy, and is also known for his studies of astrophysics, heat transfer, terrestrial magnetism, and the aurora borealis.

In 1852, Ångström formulated in Optiska undersökningar,[6] in English translation Optical Researches,[7] 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 solar radiation that expressed the wavelengths of electromagnetic radiation in the electromagnetic spectrum in multiples of one ten-millionth of a millimetre (or 10−7 mm.)[8] Since the human eye is sensitive to wavelengths from about 4000 to 7000 Å, what we commonly call visible light, that unit supported sufficiently accurate measurements of visible wavelengths without resorting to fractional numbers. The unit then spread to other sciences that deal with atomic-scale structures.

Though 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.[9]

In 1907, the International Astronomical Union defined the international ångström by declaring the wavelength of the red line of cadmium in air equal to 6438.46963 international ångströms, and this definition was endorsed by the International Bureau of Weights and Measures in 1927.[10] 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, and then the ångström was 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.[11]

Symbol

Example of the Unicode codification

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)[12]

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,[13] which gives the c- and a-axis lattice constants as 4.52 A.U. and 7.34 A.U., respectively.

See also

Look up ångström in Wiktionary, the free dictionary.

References

  1. ↑ Webster′s Encyclopedic Unabridged Dictionary of the English Language. Portland House, 1989.
  2. ↑ International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), p. 127, ISBN 92-822-2213-6
  3. ↑ Thompson, A.; Taylor, B. N (5 October 2010). "B.8 Factors for Units Listed Alphabetically". NIST Guide to the SI. NIST. Retrieved 21 September 2011.
  4. ↑ Vailionis, Arturas Ph.D. "Geometry of Crystals" (PDF). Archived from the original (PDF) on 2015-03-19. Retrieved 20 April 2015.
  5. ↑ "ICSD".
  6. ↑ "Kungliga Vetenskapsakademiens handlingar", roughly translated as Transactions of the Royal Academy of Sciences, published between 1739 and 1974, see Vetenskapsakademiens Handlingar (in Swedish).
  7. ↑ Angstrom A. J. (1855) "Optical Researches" Phil.Mag. 9. pp. 327-342.
  8. ↑ "A Brief (Incomplete) History of Light and Spectra". ChemTeam.
  9. ↑ Brand, J.C.D. (1995). Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930. CRC Press. p. 47. ISBN 9782884491631.
  10. ↑ 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
  11. ↑ 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 23 September 2011.
  12. ↑ The Unicode Consortium (2007). "Symbols" (PDF). The Unicode Standard, Version 5.0. Addison-Wesley. p. 493. ISBN 0-321-48091-0. OCLC 145867322.
  13. ↑ Bragg, W. H. (1921). "The Crystal Structure of Ice". Proceedings of the Physical Society of London 34 (1): 98.
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