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The angstrom (; ) is a unit of length equal to metre; that is, one ten- of a metre, a hundred-millionth of a centimetre, 0.1 nanometre, or 100 . The unit is named after the Swedish people physicist Anders Jonas Ångström (1814–1874). It was originally spelled with Swedish alphabet, as Ångström and later as ångström (). The latter spelling is still listed in some dictionaries, but is now rare in English language texts. Some popular US dictionaries list only the spelling angstrom.
The unit's symbol is Å, which is a letter of the Swedish alphabet, regardless of how the unit is spelled. However, "A" or "A.U." may be used in less formal contexts or typography limited media.
The angstrom is often used in the and technology to express sizes of , , microscopy structures, and lengths of , crystallography, of electromagnetic radiation, and dimensions of integrated circuit parts. The covalent radius of phosphorus, sulfur, and chlorine are about 1 angstrom, while that of hydrogen is about 0.5 angstroms. Visible light has in the range of 4000–7000 Å.
In the late 19th century, spectroscopists adopted of a metre as a convenient unit to express the wavelengths of characteristic (monochromatic components of the emission spectrum) of . 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 metre. Yet the angstrom was never part of the SI system of units, and has been increasingly replaced by the nanometre ( m) or picometre ( m).
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. From 1927 to 1960, the angstrom remained a secondary unit of length for use in spectroscopy, defined separately from the metre.
History
In 1868, Swedish people 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 .) 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 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.
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 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 mmHg under a gravity of 9.8067 m/s2).
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
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, 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 units of length, the Bohr radius—about 0.53 Å—or the much larger astronomical unit (about ).
Merriam-Webster (2024): Entry "angstrom" in the www.merriam-webster.com. Accessed 2024-01-30. Spelling "angstrom" ˈaŋ-strəm, 'ȯŋ-strəm
HarperCollins (2024): Entry "angstrom" in the 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.
Peter Roach (2011): Cambridge English Pronouncing Dictionary, 18th edition.
Arturas Vailionis (2015): " Geometry of Crystals" Lecture slides for MatSci162_172, Geometry; Stanford University.
Bureau international des poids et measures (2019): Le système international d'unités, complete brochure, 9th edition.
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
NIST (2019): Special Publication 330: The International System of Units (SI) 2019 Edition.
The 1869 edition (printed by Ferdinand Dümmler in Berlin) contains sketches of the solar spectrum.
ChemTeam (2024) A Brief (Incomplete) History of Light and Spectra, from the ChemTeam website. Accessed on 2024-07-26.
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 = ... It follows that the wavelengths of these emissions, always at 15 °C and at 760 mm, are (averages of three determinations): λR = " (where 1 μ"
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): "Comptes rendus de la 7 réunion de la Conférence générale des poids et mesures" (= "Proceedings of the 7 meeting of the General Conference of Weights and Measures"), pages 85–88.
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.
NIST CODATA - Committee on Data for Science and Technology (2024): "Angstrom star". Symbol: "Å*". Accessed on 2024-07-26.
The Unicode Consortium (2008): The Unicode Standard, Version 5.0; Chapter 15, " Symbols", page 493.
The Unicode Consortium (2021): The Unicode Standard, Version 14.0; Chapter 22.2 "Letterlike Symbols", page 839.
William H. Bragg (1921): "The Crystal Structure of Ice". Proceedings of the Physical Society of London, volume 34, issue 1, page 98
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."
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."
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)."
See also
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