Jump to content

Angstrom

From Wikipedia, the free encyclopedia
For other uses, seeAngstrom (disambiguation).
angstrom
The width of a hydrogen atom is about 1.1 angstroms; the width of a proton (in black) is1.7×10−5angstroms.
General information
Unit systemNon-SI metric unit
Unit ofLength
SymbolÅ
Named afterAnders Jonas Ångström
Conversions
1 Åin...... is equal to...
SI Units10−10m=0.1 nm
CGS Units10−8cm
Imperial units3.937008×10−9in
Planck units6.187×1024lP

Theangstrom[1][2][3][4](/ˈæŋstrəm/;[3][5][6]ANG-strəm[5]) is aunit of lengthequal to10−10m;that is, one ten-billionthof ametre,a hundred-millionth of acentimetre,[7]0.1nanometre,or 100picometres.The unit is named after theSwedishphysicistAnders Jonas Ångström(1814–1874)[7]It was originally spelled withSwedish letters,asÅngström[7]and later asångström(/ˈɒŋstrəm/).[8][9][10]The latter spelling is still listed in some dictionaries,[1]but is now rare inEnglishtexts. Some popular US dictionaries list only the spellingangstrom.[2][3]

The unit's symbol isÅ,a letter of theSwedish alphabet,no matter how the unit is spelled.[1][4][3]However, "A"[citation needed]or "A.U."[11][7]may be used in less formal contexts ortypographicallylimited media.

The angstrom is often used in thenatural sciencesandtechnologyto express sizes ofatoms,molecules,microscopic biologicalstructures, and lengths ofchemical bonds,arrangement of atoms in crystals,[12]wavelengthsofelectromagnetic radiation,and dimensions ofintegrated circuitparts. Theatomic (covalent) radiiofphosphorus,sulfur,andchlorineare about 1 angstrom, while that ofhydrogenis about 0.5 angstroms.Visible lighthaswavelengthsin the range of 4000–7000 Å.

In the late 19th century, spectroscopists adopted10−10of a metre as a convenient unit to express the wavelengths of characteristicspectral lines(monochromaticcomponents of theemission spectrum) ofchemical 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.[7]It was only in 1960, when the metre was redefined in the same way, that the angstrom became again equal to10−10metre. Yet the angstrom was never part of theSIsystem of units,[13][14]and has been increasingly replaced by the nanometre (10−9m) or picometre (10−12m).

History

[edit]
Portrait of Anders Ångström[15]

In 1868,SwedishphysicistAnders Jonas Ångströmcreated a chart of the spectrum ofsunlight,in which he expressed the wavelengths of electromagnetic radiation in theelectromagnetic spectrumin multiples of one ten-millionth of a millimetre (or10−7mm.)[16][17]Ångström's chart and table of wavelengths in the solar spectrum became widely used insolar physicscommunity, which adopted the unit and named it after him.[citation needed]It subsequently spread to the fields ofastronomical spectroscopy,atomic spectroscopy,and then to other sciences that deal with atomic-scale structures.

Early connection to the metre

[edit]

Although intended to correspond to10−10metres, that definition was not accurate enough for spectroscopy work. Until 1960 the metre was defined as the distance between two scratches on a bar ofplatinum-iridiumalloy, kept at theBIPMin 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 themetrologistHenri Trescareported it to be so incorrect that Ångström's corrected results were more in error than the uncorrected ones.[18]

Cadmium line definition

[edit]

In 1892–1895,Albert A. MichelsonandJean-René Benoît,working at the BIPM with specially developed equipment, determined that the length of the international metre standard was equal to1553163.5times the wavelength of the red line of theemission spectrumof electrically excitedcadmiumvapor.[19]In 1907, the International Union for Cooperation in Solar Research (which later became theInternational 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 760mmHgunder a gravity of 9.8067 m/s2).[20]

This definition was endorsed at the 7thGeneral Conference on Weights and Measures(CGPM) in 1927,[citation needed]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.[citation needed]

Redefinition in terms of the metre

[edit]

In 1960, the metre itself was redefined in spectroscopic terms, which allowed the angstrom to be redefined as being exactly 0.1 nanometres.[citation needed]

Angstrom star

[edit]

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 theAngstrom Star(symbol: Å*) as 0.202901 times the wavelength of the tungstenline.[15][22]This auxiliary unit was intended to be accurate to within 5parts per millionof 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.[23]

Current status

[edit]

Although still widely used in physics and chemistry, the angstrom is not officially a part of theInternational System of Units(SI). Up to 2019, it was listed as a compatible unit by both theInternational Bureau of Weights and Measures(BIPM) and the USNational Institute of Standards and Technology(NIST).[8][10]However, it is not even mentioned in the 9th edition of the official SI standard, the "BIPM Brochure" (2019)[13]or in the NIST version of the same.,[14]and BIPM officially discourages its use. The angstrom is also not included in theEuropean Union's catalogue of units of measurethat may be used within its internal market.[24]

Symbol

[edit]
Unicodecodification. The third option shall not be used anymore.

For compatibility reasons,Unicodeassigns a code pointU+212BÅANGSTROM SIGNfor the angstrom symbol, which is accessible inHTMLas theentityÅ,Å,orÅ.[25]However, version 5 of the standard already deprecates that code point and has itnormalizedinto the code for the Swedish letterU+00C5ÅLATIN CAPITAL LETTER A WITH RING ABOVE(HTML entityÅ,Å,orÅ), which should be used instead.[26][25]

In older publications, where the Åglyphwas unavailable, the unit was sometimes written as "A.U.". An example isBragg's 1921 classical paper on the structure of ice,[11]which gives the c- and a-axislattice constantsas 4.52 A.U. and 7.34 A.U., respectively. Ambiguously, the abbreviation "a.u."may also refer to theatomic unitof length, thebohr—about 0.53 Å—or the much largerastronomical unit(about1.5×1011m).[27][28][29]

See also

[edit]

References

[edit]
  1. ^abcOxford University Press (2019) Entry "angstrom" byOxford Living Dictionariesonline;Archived on 2019-03-06.Spellings "angstrom" [aŋstrəm] and "ångström"; symbol "Å"
  2. ^abMerriam-Webster (2024):Entry "angstrom"in the [www.merriam-webster.comMerriam-Webster.com Dictionary]. Accessed 2024-01-30. Spelling "angstrom" [ˈaŋ-strəm], ['ȯŋ-strəm]
  3. ^abcdHarperCollins (2024):Entry "angstrom"in theCollins English Dictionaryonline.Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A".
  4. ^abMerriam-Webster (1989):Webster's Encyclopedic Unabridged Dictionary of the English Language.Portland House, 1989
  5. ^abJohn C. Wells (2008):Longman Pronunciation Dictionary,3rd edition.ISBN9781405881180
  6. ^Peter Roach (2011):Cambridge English Pronouncing Dictionary,18th edition.ISBN9780521152532
  7. ^abcdeOxford University Press (1986) Entry "Ångström (unit)" in theOxford 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 10−8cm. "
  8. ^abInternational Bureau of Weights and Measures(2006),The International System of Units (SI)(PDF)(8th ed.), p. 127,ISBN92-822-2213-6,archived(PDF)from the original on 2021-06-04,retrieved2021-12-16
  9. ^IUPAC,Compendium of Chemical Terminology,2nd ed. (the "Gold Book" ) (1997). Online corrected version: (2006–) "Ångström".doi:10.1351/goldbook.N00350
  10. ^abAmbler 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. ^abWilliam H. Bragg (1921):"The Crystal Structure of Ice".Proceedings of the Physical Society of London,volume 34, issue 1, page 98doi:10.1088/1478-7814/34/1/322
  12. ^Arturas Vailionis (2015): "Geometry of Crystals"Lecture slides for MatSci162_172, Geometry; Stanford University.Archived on 2015-03-19
  13. ^abBureau international des poids et measures (2019):Le système international d'unités,complete brochure, 9th edition.
  14. ^abNIST (2019):Special Publication 330: The International System of Units (SI) 2019 Edition.
  15. ^abJ. 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
  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) containssketches of the solar spectrum.
  17. ^ChemTeam (2024)A Brief (Incomplete) History of Light and Spectra,from theChemTeamwebsite. Accessed on 2024-07-26.
  18. ^Brand, John C. D. (1995).Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930.CRC Press. p. 47.ISBN9782884491631.
  19. ^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 =1×10−6m] "
  20. ^Jean-René Benoît,Charles Fabry,andAlfred 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.
  21. ^Bureau international des poids et measures (1927):"Comptes rendus de la 7eréunion de la Conférence générale des poids et mesures "(= "Proceedings of the 7thmeeting of the General Conference of Weights and Measures "), pages 85–88.Archived on 2018-11-18
  22. ^NIST CODATA - Committee on Data for Science and Technology (2024):"Angstrom star".Symbol: "Å*". Accessed on 2024-07-26.
  23. ^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.
  24. ^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.
  25. ^abThe Unicode Consortium (2021):The Unicode Standard, Version 14.0;Chapter 22.2 "Letterlike Symbols", page 839.ISBN978-1-936213-29-0
  26. ^The Unicode Consortium (2008):The Unicode Standard, Version 5.0;Chapter 15, "Symbols",page 493.ISBN978-0-321-48091-0
  27. ^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."
  28. ^Oxford Journals (2012): "Instructions for Authors".Monthly Notices of the Royal Astronomical Society.Archived on 22 October 2012Quote: "The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc."
  29. ^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)."
[edit]
Look upangstromin Wiktionary, the free dictionary.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Angstrom&oldid=1243110314"