{{Other uses}} {{Short description|Unit of length}} {{infobox unit | name = angstrom | image = Hydrogen atom.svg | caption = The width of a hydrogen atom is about 1.1 angstroms; the width of a proton (in black) is {{val|1.7|e=-5|}} angstroms. | standard = Non-SI metric unit | quantity = [[Length]] | symbol = Å | namedafter = [[Anders Jonas Ångström]] | units1 = [[SI Units]] | inunits1 = {{val|e=-10|u=m}} = {{val|0.1|u=nm}} | units2 = [[CGS Units]] | inunits2 = {{val|e=-8|u=cm}} | units3 = [[Imperial units]] | inunits3= {{cvt|1|Å|in|disp=out|sigfig=7}} | units4 = [[Planck units]] | inunits4 = {{val|6.187|e=24|u=''l''P}} }} The '''angstrom''' ({{IPAc-en|ˈ|æ|ŋ|s|t|r|əm}}; {{respell|ANG|strəm}}) or '''ångström''' ({{IPAc-en|ˈ|ɒ|ŋ|s|t|r|əm}}) is a [[metric units|metric]] [[unit of length]] equal to {{val|e=-10}} [[metre|m]]; that is, one ten-billionth ([[short and long scale|US]]) of a [[metre]], a hundred-millionth of a [[centimetre]], 0.1 [[nanometre]], or 100 [[picometre]]s. Its symbol is [[Å]], a letter of the [[Swedish alphabet]]. The unit is named after the [[Swedish people|Swedish]] physicist [[Anders Jonas Ångström]] (1814–1874). The angstrom is often used in the [[natural science]]s and [[technology]] to express sizes of [[atom]]s, [[molecule]]s, microscopic biological structures, and lengths of [[chemical bond]]s, [[crystallography|arrangement of atoms in crystals]], [[wavelength]]s of [[electromagnetic radiation]], and dimensions of [[integrated circuit]] parts. The [[covalent radius|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 {{val|e=-10}} of a metre as a convenient unit to express the wavelengths of characteristic [[spectral line]]s ([[monochromatic radiation|monochromatic]] components of the [[emission spectrum]]) of [[chemical element]]s. 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. It was only in 1960, when the metre was redefined in the same way, that the angstrom became again equal to {{val|e=-10}} metre. Even though it is a decimal power fraction of the metre, the angstrom was never part of the [[SI]] system of units, 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), but it is not mentioned in the 9th edition of the official SI document, the "BIPM Brochure" (2019) or in the NIST version of the same. The 8th edition of the BIPM brochure (2006) and the NIST guide 811 (2008) used the spelling ''ångström'', with Swedish letters; however, this form is rare in [[English language|English]] texts. Some popular US dictionaries list only the spelling ''angstrom''. The accepted symbol is "Å", no matter how the unit is spelled. However, "A" is often used in less formal contexts or [[typography|typographically]] limited media.{{citation needed|date=April 2020}} ==History== [[File:Anders Ångström painting.jpg|thumb|Portrait of Anders Ångström]] In 1868, [[Swedish people|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 {{val|e=-7|u=mm}}.) 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.{{citation needed|date=April 2020}} 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 {{val|e=-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 [[International Bureau of Weights and Measures|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. 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 {{gaps|1|553|163.5}} times the wavelength of the red line of the [[emission spectrum]] of electrically excited [[cadmium]] vapor. 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 [[millimetres of mercury|mmHg]] under a gravity of 9.8067 m/s2). This definition was endorsed at the 7th [[General Conference on Weights and Measures]] (CGPM) in 1927,{{citation needed|date=April 2020}} but the material definition of the metre was retained until 1960. From 1927 to 1960, the angstrom remained a secondary unit of length for use in spectroscopy, defined separately from the metre.{{citation needed|date=November 2021}} 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|date=April 2020}} 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]] ({{val|e=-9|u=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 units of measurement directives|European Union's catalogue of units of measure]] that may be used within its internal market. ==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 which gives the c- and a-axis lattice constants as 4.52 A.U. and 7.34 A.U., respectively. Ambiguously, the abbreviation "[[Au (disambiguation)#Physics and chemistry|a.u.]]" may also refer to the [[Atomic units|atomic unit]] of length, the [[Bohr radius|bohr]]—about 0.53 Å—or the much larger [[astronomical unit]] (about {{val|1.5|e=11|u=m}}). 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 people|Swedish]] physicist [[Anders Jonas Ångström]] (1814–1874). ==See also== * {{Section link|Orders of magnitude (length)#100 picometres}} (for objects on this scale) * [[Conversion of units]] * [[X unit]] ==References== Oxford University Press (2019) Entry "angstrom" by ''Oxford Living Dictionaries'' online; [https://web.archive.org/web/20190306044036/https://en.oxforddictionaries.com/definition/angstrom Archived on 2019-03-06]. Spellings "angstrom" [aŋstrəm] and "ångström"; symbol "Å" Oxford University Press (1986) Entry "Ångström (unit)" in the ''Oxford English Dictionary'', 2nd edition (1986); [https://web.archive.org/web/20211122223411/https://www.oed.com/oed2/00008552 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." Merriam-Webster (2024): [https://www.merriam-webster.com/dictionary/angstrom Entry "angstrom"] in the [www.merriam-webster.com ''Merriam-Webster.com Dictionary'']. Accessed 2024-01-30. Spelling "ang​strom" [ˈaŋ-strəm], ['ȯŋ-strəm] Merriam-Webster (1989): ''Webster's Encyclopedic Unabridged Dictionary of the English Language''. Portland House, 1989 HarperCollins (2024): [https://www.collinsdictionary.com/dictionary/english/angstrom Entry "angstrom"] in the [https://www.collinsdictionary.com/ ''Collins English Dictionary'' online]. Accessed on 2024-07-26. Spelling "angstrom" [ˈæŋstrʌm], [æŋstrəm]; symbols "Å", "A". John C. Wells (2008): ''Longman Pronunciation Dictionary'', 3rd edition. {{isbn|9781405881180}} Peter Roach (2011): ''Cambridge English Pronouncing Dictionary'', 18th edition. {{isbn|9780521152532}} {{GoldBookRef|title=Ångström|file=N00350}} Arturas Vailionis (2015): "[https://web.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/02_Geometry,%20RecLattice.pdf Geometry of Crystals]" Lecture slides for MatSci162_172, Geometry; Stanford University. [https://web.archive.org/web/20150319042436/https://web.stanford.edu/group/glam/xlab/MatSci162_172/LectureNotes/02_Geometry,%20RecLattice.pdf Archived on 2015-03-19] {{SIBrochure8th |page=127}} Bureau international des poids et measures (2019): [https://www.bipm.org/documents/20126/41483022/SI-Brochure-9.pdf/fcf090b2-04e6-88cc-1149-c3e029ad8232 Le système international d'unités], complete brochure, 9th edition. Ambler Thompson and Barry N. Taylor (2009): "[https://www.nist.gov/physical-measurement-laboratory/nist-guide-si-appendix-b8 B.8 Factors for Units Listed Alphabetically]". ''NIST Guide to the SI'', National Institutes of Standards and Technology. Accessed on 2019-03-02 NIST (2019): ''[https://www.nist.gov/pml/special-publication-330 Special Publication 330: The International System of Units (SI) 2019 Edition]''. {{cite book |last1=Ångström |first1=A.J. |title=Recherches sur le spectre solaire |trans-title=Investigations of the solar spectrum |date=1868 |publisher=W. Schultz |location=Uppsala, Sweden |url=https://archive.org/details/recherchessurle00nggoog/page/n3 |language=fr}} The 1869 edition (printed by Ferdinand Dümmler in Berlin) contains [https://books.google.com/books?id=JDtTWs0zJDEC&pg=PT3 sketches of the solar spectrum.] (2024)[https://www.chemteam.info/Electrons/Spectrum-History2.html ''A Brief (Incomplete) History of Light and Spectra''], from the [https://www.chemteam.info/ChemTeamIndex.html ChemTeam] website. Acessed on 2024-07-26. {{cite book |last=Brand |first=John C. D. |title=Lines of Light: Sources of Dispersive Spectroscopy, 1800-1930 |date=1995 |publisher=CRC Press |isbn=9782884491631 |page=47 |url=https://books.google.com/books?id=sKx0IBC22p4C&q=meter+bar+angstrom&pg=PA47 }} {{cite journal |last1=Michelson |first1=Albert A. |translator-last=Benoît |translator-first=Jean-René |title=Détermination expérimentale de la valeur du mètre en longueurs d'ondes lumineuses |journal=Travaux et Mémoires du Bureau International des Poids et Mesures |date=1895 |volume=11 |pages=1–85 |url=https://babel.hathitrust.org/cgi/pt?id=hvd.hxh7er;view=1up;seq=17 |trans-title=Experimental determination of the value of the meter in terms of the lengths of light waves |language=fr}} 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 = {{gaps|1|553|163,5|''λ''R}} ... It follows that the wavelengths of these emissions, always at 15 °C and at 760 mm, are (averages of three determinations): ''λ''R = {{gaps|0,643|847|22|μ}}" (where [1 μ = {{val|1|e=-6|u=m}}]" 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. Bureau international des poids et measures (1927): [https://www.bipm.org/utils/common/pdf/CGPM/CGPM7.pdf#page=87 "Comptes rendus de la 7{{sup|e}} réunion de la Conférence générale des poids et mesures"] (= "Proceedings of the 7{{sup|th}} meeting of the General Conference of Weights and Measures"), pages 85–88. [https://web.archive.org/web/20181118214334/https://www.bipm.org/utils/common/pdf/CGPM/CGPM7.pdf#page=87 Archived on 2018-11-18] Council of the European Communities (1979): [http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=CONSLEG:1980L0181:20090527:EN:PDF "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. NIST CODATA - Committee on Data for Science and Technology (2024): [https://physics.nist.gov/cgi-bin/cuu/Value?angstar "Angstrom star"]. Symbol: "Å*". Accessed on 2024-07-26. {{cite report |last1=Curtis |first1=I.|last2=Morgan|first2=I. |last3=Hart |first3=M.|last4=Milne|first4=A.D.|date=August 1971 |editor1-last=Langenberg|editor1-first=D. N.|editor2-last=Taylor|editor2-first=B.N.|title=Proceedings of the International Congress on Precision Measurement and Fundamental Constants |chapter=A New Determination of Avogadro's Number |publisher= National Bureau of Standards |page= 285|volume=343}} The Unicode Consortium (2008): ''[https://www.unicode.org/versions/Unicode5.0.0/ The Unicode Standard, Version 5.0]''; Chapter 15, "[https://www.unicode.org/versions/Unicode5.0.0/ch15.pdf Symbols]". {{isbn|978-0-321-48091-0}} The Unicode Consortium (2021): [https://www.unicode.org/versions/Unicode14.0.0/UnicodeStandard-14.0.pdf ''The Unicode Standard, Version 14.0'']; Chapter 22.2 "Letterlike Symbols", page 839. {{isbn|978-1-936213-29-0}} [[William H. Bragg]] (1921): [https://iopscience.iop.org/article/10.1088/1478-7814/34/1/322 "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}} International Astronomical Union (2012): "[https://www.iau.org/static/resolutions/IAU2012_English.pdf 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." Oxford Journals (2012): "Instructions for Authors". ''Monthly Notices of the Royal Astronomical Society''. [https://web.archive.org/web/20121022064348/http://www.oxfordjournals.org/our_journals/mnras/for_authors/#6.4%20Miscellaneous%20journal%20style Archived on 22 October 2012] Quote: "The units of length/distance are Å, nm, μm, mm, cm, m, km, au, light-year, pc." American Astronomical Society (2016): "Manuscript Preparation: AJ & ApJ Author Instructions". [https://web.archive.org/web/20160221121728/http://aas.org/authors/manuscript-preparation-aj-apj-author-instructions#_Toc2.2 Archived on 2016-02-21]. Quote: "Use standard abbreviations for ... natural units (e.g., au, pc, cm)." ==External links== {{wiktionary}} {{DEFAULTSORT:Angstrom}} [[Category:Non-SI metric units]] [[Category:Units of length]]