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Angstrom
Unit of length; equals 0.1 nanometre

The angstrom is a unit of length equal to 10⁻¹⁰ meters, or one ten-billionth of a meter. Named after the Swedish physicist Anders Jonas Ångström, its symbol is Å. The angstrom is widely used in the natural sciences and technology to measure atomic and molecular sizes, lengths of chemical bonds, and wavelengths of electromagnetic radiation. For example, the atomic radii of elements like phosphorus and sulfur are about 1 angstrom. Though convenient, the angstrom is not part of the SI system and is increasingly replaced by the nanometre or picometre.

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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.)2728 Ångström's chart and table of wavelengths in the solar spectrum became widely used in the 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.

Early connection to the metre

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.29

Cadmium line definition

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.30 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).31

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 1960.32 From 1927 to 1960, the angstrom remained a secondary unit of length for use in spectroscopy, defined separately from the metre.

Redefinition in terms of 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.

Angstrom star

After the redefinition of the metre in spectroscopic terms, the Angstrom was formally redefined to be 0.1 nanometres. 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 κ α 1 {\textstyle \kappa _{\alpha 1}} line.3334 This auxiliary unit was intended to be accurate to within 5 parts per million of the version derived from the new metre. 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.35

Current status

Although still widely used in physics and chemistry, the angstrom is not officially a part of the International System of Units (SI). 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).3637 However, it is not mentioned in the 9th edition of the official SI standard, the "BIPM Brochure" (2019)38 or in the NIST version of the same,39 and BIPM officially discourages its use. The angstrom is also not included in the European Union's catalogue of units of measure that may be used within its internal market.40

Symbol

For compatibility reasons, Unicode assigns a code point U+212B Å ANGSTROM SIGN for the angstrom symbol, which is accessible in HTML as the entity Å, Å, or Å.41 However, version 5 of the standard already deprecates that code point and has it normalized into the code for the Swedish letter U+00C5 Å LATIN CAPITAL LETTER A WITH RING ABOVE (HTML entity Å, Å, or Å), which should be used instead.4243

In older publications, where the Å glyph was unavailable, the unit was sometimes written as "A.U.". An example is Bragg's 1921 classical paper on the structure of ice,44 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).454647

See also

Look up angstrom in Wiktionary, the free dictionary.

References

  1. Oxford University Press (2019) Entry "angstrom" by Oxford Living Dictionaries online; Archived on 2019-03-06. Spellings "angstrom" [aŋstrəm] and "ångström"; symbol "Å" https://web.archive.org/web/20190306044036/https://en.oxforddictionaries.com/definition/angstrom ↩

  2. Merriam-Webster (2024): Entry "angstrom" in the [www.merriam-webster.com Merriam-Webster.com Dictionary]. Accessed 2024-01-30. Spelling "angstrom" [ˈaŋ-strəm], ['ȯŋ-strəm] https://www.merriam-webster.com/dictionary/angstrom ↩

  3. HarperCollins (2024): Entry "angstrom" in the Collins English Dictionary online. Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A". https://www.collinsdictionary.com/dictionary/english/angstrom ↩

  4. Merriam-Webster (1989): Webster's Encyclopedic Unabridged Dictionary of the English Language. Portland House, 1989 ↩

  5. HarperCollins (2024): Entry "angstrom" in the Collins English Dictionary online. Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A". https://www.collinsdictionary.com/dictionary/english/angstrom ↩

  6. John C. Wells (2008): Longman Pronunciation Dictionary, 3rd edition. ISBN 9781405881180 /wiki/ISBN_(identifier) ↩

  7. Peter Roach (2011): Cambridge English Pronouncing Dictionary, 18th edition. ISBN 9780521152532 /wiki/ISBN_(identifier) ↩

  8. John C. Wells (2008): Longman Pronunciation Dictionary, 3rd edition. ISBN 9781405881180 /wiki/ISBN_(identifier) ↩

  9. Oxford University Press (1986) Entry "Ångström (unit)" in the Oxford English Dictionary, 2nd edition (1986); Archived on 2021-11-22. Spellings "Ångström" [ɔːŋstrœm] (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10−8 cm." https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 ↩

  10. Oxford University Press (1986) Entry "Ångström (unit)" in the Oxford English Dictionary, 2nd edition (1986); Archived on 2021-11-22. Spellings "Ångström" [ɔːŋstrœm] (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10−8 cm." https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 ↩

  11. Oxford University Press (1986) Entry "Ångström (unit)" in the Oxford English Dictionary, 2nd edition (1986); Archived on 2021-11-22. Spellings "Ångström" [ɔːŋstrœm] (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10−8 cm." https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 ↩

  12. 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 92-822-2213-6 ↩

  13. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Ångström". doi:10.1351/goldbook.N00350 /wiki/International_Union_of_Pure_and_Applied_Chemistry ↩

  14. 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 https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b8 ↩

  15. Oxford University Press (2019) Entry "angstrom" by Oxford Living Dictionaries online; Archived on 2019-03-06. Spellings "angstrom" [aŋstrəm] and "ångström"; symbol "Å" https://web.archive.org/web/20190306044036/https://en.oxforddictionaries.com/definition/angstrom ↩

  16. Merriam-Webster (2024): Entry "angstrom" in the [www.merriam-webster.com Merriam-Webster.com Dictionary]. Accessed 2024-01-30. Spelling "angstrom" [ˈaŋ-strəm], ['ȯŋ-strəm] https://www.merriam-webster.com/dictionary/angstrom ↩

  17. HarperCollins (2024): Entry "angstrom" in the Collins English Dictionary online. Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A". https://www.collinsdictionary.com/dictionary/english/angstrom ↩

  18. Oxford University Press (2019) Entry "angstrom" by Oxford Living Dictionaries online; Archived on 2019-03-06. Spellings "angstrom" [aŋstrəm] and "ångström"; symbol "Å" https://web.archive.org/web/20190306044036/https://en.oxforddictionaries.com/definition/angstrom ↩

  19. Merriam-Webster (1989): Webster's Encyclopedic Unabridged Dictionary of the English Language. Portland House, 1989 ↩

  20. HarperCollins (2024): Entry "angstrom" in the Collins English Dictionary online. Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A". https://www.collinsdictionary.com/dictionary/english/angstrom ↩

  21. William H. Bragg (1921): "The Crystal Structure of Ice". Proceedings of the Physical Society of London, volume 34, issue 1, page 98 doi:10.1088/1478-7814/34/1/322 https://iopscience.iop.org/article/10.1088/1478-7814/34/1/322 ↩

  22. Oxford University Press (1986) Entry "Ångström (unit)" in the Oxford English Dictionary, 2nd edition (1986); Archived on 2021-11-22. Spellings "Ångström" [ɔːŋstrœm] (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10−8 cm." https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 ↩

  23. Arturas Vailionis (2015): "Geometry of Crystals" Lecture slides for MatSci162_172, Geometry; Stanford University. Archived on 2015-03-19 https://web.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/02_Geometry,%20RecLattice.pdf ↩

  24. Oxford University Press (1986) Entry "Ångström (unit)" in the Oxford English Dictionary, 2nd edition (1986); Archived on 2021-11-22. Spellings "Ångström" [ɔːŋstrœm] (capitalized) and "angstrom" (lowercase); symbols "Å", "Å.U.", "A.U." Quote: "The International Ångström (I.Å.) was defined in 1907 in terms of the wavelength of cadmium which in standard conditions is 6438·4696 I.Å. When the metre was defined in terms of the wavelength of krypton in 1960 the Ångström became exactly equal to 10−8 cm." https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 ↩

  25. Bureau international des poids et measures (2019): Le système international d'unités, complete brochure, 9th edition. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 ↩

  26. NIST (2019): Special Publication 330: The International System of Units (SI) 2019 Edition. https://www.nist.gov/pml/special-publication-330 ↩

  27. 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. https://archive.org/details/recherchessurle00nggoog/page/n3 ↩

  28. ChemTeam (2024)A Brief (Incomplete) History of Light and Spectra, from the ChemTeam website. Accessed on 2024-07-26. https://www.chemteam.info/Electrons/Spectrum-History2.html ↩

  29. Brand, John C. D. (1995). Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930. CRC Press. p. 47. ISBN 9782884491631. 9782884491631 ↩

  30. Albert A. Michelson (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"); translated to French by Jean-René Benoît. Travaux et Mémoires du Bureau International des Poids et Mesures, volume 11, pages 1–85. Quote from p. 85, back-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]" https://babel.hathitrust.org/cgi/pt?id=hvd.hxh7er ↩

  31. Jean-René Benoît, Charles Fabry, and Alfred Pérot (1907): "Nouvelle Détermination du mètre en longueurs d'ondes lumineuses" (= "A new determination of the metre in terms of the wavelength of light"). Comptes rendus hebdomadaires des séances de l'Académie des sciences, volume 144, pages 1082-1086. /wiki/Charles_Fabry ↩

  32. Bureau international des poids et measures (1927): "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"), pages 85–88. Archived on 2018-11-18 https://www.bipm.org/utils/common/pdf/CGPM/CGPM7.pdf#page=87 ↩

  33. J. A. Bearden (1965): "Selection of the W Kα₁ as the X-Ray Wavelength Standard". Physical Review 2nd series, volume 137, issue 2B, pages 455B–B461. doi:10.1103/PhysRev.137.B455 /wiki/Doi_(identifier) ↩

  34. NIST CODATA - Committee on Data for Science and Technology (2024): "Angstrom star". Symbol: "Å*". Accessed on 2024-07-26. https://physics.nist.gov/cgi-bin/cuu/Value?angstar ↩

  35. 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. ↩

  36. 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 92-822-2213-6 ↩

  37. 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 https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b8 ↩

  38. Bureau international des poids et measures (2019): Le système international d'unités, complete brochure, 9th edition. https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 ↩

  39. NIST (2019): Special Publication 330: The International System of Units (SI) 2019 Edition. https://www.nist.gov/pml/special-publication-330 ↩

  40. Council of the European Communities (1979): "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". Accessed on 2011-09-23. http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:20090527:EN:PDF ↩

  41. The Unicode Consortium (2021): The Unicode Standard, Version 14.0; Chapter 22.2 "Letterlike Symbols", page 839. ISBN 978-1-936213-29-0 https://www.unicode.org/versions/Unicode14.0.0/UnicodeStandard-14.0.pdf ↩

  42. The Unicode Consortium (2008): The Unicode Standard, Version 5.0; Chapter 15, "Symbols", page 493. ISBN 978-0-321-48091-0 https://www.unicode.org/versions/Unicode5.0.0/ ↩

  43. The Unicode Consortium (2021): The Unicode Standard, Version 14.0; Chapter 22.2 "Letterlike Symbols", page 839. ISBN 978-1-936213-29-0 https://www.unicode.org/versions/Unicode14.0.0/UnicodeStandard-14.0.pdf ↩

  44. William H. Bragg (1921): "The Crystal Structure of Ice". Proceedings of the Physical Society of London, volume 34, issue 1, page 98 doi:10.1088/1478-7814/34/1/322 https://iopscience.iop.org/article/10.1088/1478-7814/34/1/322 ↩

  45. International Astronomical Union (2012): "Resolution B2: On the re-definition of the astronomical unit of length". Proceedings of the XXVIII General Assembly of International Astronomical Union, Beijing, China. Quote: "... recommends ... 5. that the unique symbol 'au' be used for the astronomical unit." https://www.iau.org/static/resolutions/IAU2012_English.pdf ↩

  46. Oxford Journals (2012): "Instructions for Authors". Monthly Notices of the Royal Astronomical Society. Archived on 22 October 2012 Quote: "The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc." https://web.archive.org/web/20121022064348/http://www.oxfordjournals.org/our_journals/mnras/for_authors/#6.4%20Miscellaneous%20journal%20style ↩

  47. American Astronomical Society (2016): "Manuscript Preparation: AJ & ApJ Author Instructions". Archived on 2016-02-21. Quote: "Use standard abbreviations for ... natural units (e.g., au, pc, cm)." https://web.archive.org/web/20160221121728/http://aas.org/authors/manuscript-preparation-aj-apj-author-instructions#_Toc2.2 ↩