Angstrom

{{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'''<ref name=oxfo2019/><ref name=webs2024/><ref name=collins/><ref name=webs1989/> ({{IPAc-en|ˈ|æ|ŋ|.|s|t|r|əm}};<ref name=collins/><ref name=well2008/><ref name=roac2011/> {{respell|ANG|strəm}}<ref name=well2008/>) is a unit of length equal to {{val|e=-10}} m; that is, one ten-billionth of a metre, a hundred-millionth of a centimetre,<ref name=oxfo1986/> 0.1 nanometre, or 100 picometres. The unit is named after the Swedish physicist Anders Jonas Ångström (1814–1874).<ref name=oxfo1986/> It was originally spelled with Swedish letters, as '''Ångström'''<ref name=oxfo1986/> and later as '''ångström''' ({{IPAc-en|ˈ|ɒ|ŋ|.|s|t|r|əm}}).<ref name=bipm8/><ref name=iupac/><ref name=thom2009/> The latter spelling is still listed in some dictionaries,<ref name=oxfo2019/> but is now rare in English texts. Some popular US dictionaries list only the spelling ''angstrom''.<ref name=webs2024/><ref name=collins/>

The unit's symbol is Å, which is a letter of the Swedish alphabet, regardless of how the unit is spelled.<ref name=oxfo2019/><ref name=webs1989/> However, "A"<ref name=collins/> or "A.U."<ref name=brag1921/><ref name=oxfo1986/> (not to be confused with an astronomical unit, which has the same initials and therefore abbreviation) may be used in less formal contexts or typographically limited media.

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,<ref name=vail2015/> 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 {{val|e=-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.<ref name=oxfo1986/> 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. Yet the angstrom was never part of the SI system of units,<ref name=bipm9/><ref name=nist2019/> and has been increasingly replaced by the nanometre ({{val |e=-9 |u=m}}) or picometre ({{val |e=-12 |u=m}}).

==History== thumb|Portrait of Anders Ångström<ref name=bear1965/> 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 {{val|e=-7|u=mm}}.)<ref name=angs1868/><ref name=chemteam/> 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.{{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.

===Early connection to the metre=== 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 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.<ref name=bran1995/>

===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 {{gaps|1|553|163.5}} times the wavelength of the red line of the emission spectrum of electrically excited cadmium vapor.<ref name=beno1895/> 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).<ref name=beno1907/>

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.<ref name=bipm1927/> 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}}

===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.{{citation needed|date=April 2020}}

===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 <math display="inline>\kappa_{\alpha 1}</math> line.<ref name=bear1965/><ref name=coda2024/> 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.<ref name=curt1971/>

===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).<ref name=bipm8/><ref name=thom2009/> However, it is not mentioned in the 9th edition of the official SI standard, the "BIPM Brochure" (2019)<ref name=bipm9/> or in the NIST version of the same,<ref name=nist2019/> 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.<ref name=EEC1979/>

==Symbol== [[File:Angstrom unicode sample.svg|thumb|Unicode codification. The third option shall not be used anymore.]]

For compatibility reasons, Unicode assigns a code point {{unichar|212B}} for the angstrom symbol, which is accessible in HTML as the entity <code>&angst;</code>, <code>&#x0212B;</code>, or <code>&#8491;</code>.<ref name=unicode14/> However, version 5 of the standard already deprecates that code point and has it normalized into the code for the Swedish letter {{unichar|00C5}} (HTML entity <code>&Aring;</code>, <code>&#xC5;</code>, or <code>&#197;</code>), which should be used instead.<ref name=unicode5/><ref name=unicode14/>

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,<ref name=brag1921/> 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 {{val|1.5|e=11|u=m}}).<ref name=IAU2012/><ref name=MNRAS2012/><ref name=AAS2016/>

==See also== * {{Section link|Orders of magnitude (length)#100 picometres}} (for objects on this scale) * Conversion of units * X unit

==References== <references>

<ref name=oxfo2019>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"</ref>

<ref name=oxfo1986>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."</ref>

<ref name=webs2024>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 "angstrom" [ˈaŋ-strəm], ['ȯŋ-strəm]</ref>

<ref name=webs1989>Merriam-Webster (1989): ''Webster's Encyclopedic Unabridged Dictionary of the English Language''. Portland House, 1989</ref>

<ref name=collins>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".</ref>

<ref name=well2008>John C. Wells (2008): ''Longman Pronunciation Dictionary'', 3rd edition. {{isbn|9781405881180}}</ref>

<ref name=roac2011>Peter Roach (2011): ''Cambridge English Pronouncing Dictionary'', 18th edition. {{isbn|9780521152532}}</ref>

<ref name=iupac>{{GoldBookRef|title=Ångström|file=N00350}}</ref>

<ref name=vail2015>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]</ref>

<ref name=bipm8>{{SIBrochure8th |page=127}}</ref>

<ref name=bipm9>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.</ref>

<ref name=thom2009>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</ref>

<ref name=nist2019>NIST (2019): ''[https://www.nist.gov/pml/special-publication-330 Special Publication 330: The International System of Units (SI) 2019 Edition]''.</ref>

<ref name=angs1868>{{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.]</ref>

<ref name=chemteam>ChemTeam (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. Accessed on 2024-07-26.</ref>

<ref name=bear1965>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}}</ref>

<ref name=bran1995>{{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 }}</ref>

<ref name=beno1895>Albert A. Michelson (1895): "[https://babel.hathitrust.org/cgi/pt?id=hvd.hxh7er 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 = {{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}}]"</ref>

<ref name=beno1907>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.</ref>

<ref name=bipm1927>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]</ref>

<ref name=EEC1979>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.</ref>

<ref name=coda2024>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.</ref>

<ref name=curt1971>{{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}}</ref>

<ref name=unicode5>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]", page 493. {{isbn|978-0-321-48091-0}}</ref>

<ref name=unicode14>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}}</ref>

<ref name=brag1921>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}}</ref>

<ref name=IAU2012>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."</ref>

<ref name=MNRAS2012>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."</ref>

<ref name=AAS2016>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)."</ref>

</references>

==External links== {{wiktionary}}

Category:Non-SI metric units Category:Units of length