On this page
Chemistry and physics books often give atomic sizes and wavelengths in ångströms, written Å. The unit is named after a Swedish physicist who spent years measuring the dark lines in sunlight more precisely than anyone before him. This post covers who Anders Ångström was, what he found, and a short worked example using the unit.
Who was Anders Ångström?
The most detailed early account is his obituary in the Proceedings of the Royal Society, published in 1877. It says Ångström was born on 13 August 1814 at the Lögdö works in Medelpad, in northern Sweden, where his father was a chaplain. He studied at Uppsala, took his doctorate in 1839 and taught there for the rest of his life.
With no opening in physics, he first worked in astronomy, spending 1842 at the Stockholm Observatory, and made many magnetic measurements across Sweden. He later became Professor of Physics at Uppsala and served as the university's Rector in 1870 and 1871. The Royal Society elected him a Foreign Member in 1870 and awarded him its Rumford Medal. He died on 21 June 1874.
What did his 1853 Optical Researches show?
The obituary singles out a memoir called Optical Researches, presented to the Stockholm Academy of Sciences in 1853. In it Ångström showed three things:
The spectrum of an electric spark is two spectra laid on top of each other: one from the metal of the electrodes and one from the gas the spark passes through.
The spark spectrum of an alloy of two metals contains the spectrum of each metal.
A vapour or gas can absorb only the kinds of light it gives out when it is very hot.
The last idea links bright emission lines to dark absorption lines. When Ångström was elected to the Royal Society, Sir Edward Sabine remarked, as the obituary records, that this memoir contained the basic principles of all later progress in spectrum analysis. Gustav Kirchhoff later turned the link between emission and absorption into a law; our post on Kirchhoff and spectroscopy tells that part.
How did he measure the solar spectrum?
Through the 1860s Ångström published a series of studies, listed in the obituary: a memoir on the lines of the solar spectrum in 1861, a new determination of the wavelengths of light in 1863, and a study of the violet end of the solar spectrum with Tobias Thalén in 1865.
These led to his major work of 1868, Researches on the Solar Spectrum. The obituary describes it as giving wavelengths for the Fraunhofer lines "founded on exact measurements". He was also the first to examine the spectrum of the aurora borealis.
Where does the ångström fit today?
The NIST Guide to the SI lists the ångström as Å = 0.1 nm = 10⁻¹⁰ m. It is one of a few non-SI units the international committee on weights and measures allowed to continue in use in 1978. NIST discourages it in new work, but you will still meet it in X-ray work, crystal structures and bond lengths.
A worked example: from a grating to ångströms
The numbers here are sample numbers for practice. A diffraction grating has 600 lines per millimetre. A bright line appears in first order at θ = 20.7°. Find its wavelength in nanometres and ångströms.
Line spacing: d = 1/600 mm = 1.667 × 10⁻³ mm = 1.667 × 10⁻⁶ m.
Grating equation for first order (m = 1): λ = d sin θ.
sin 20.7° = 0.3535, so λ = 1.667 × 10⁻⁶ × 0.3535 = 5.89 × 10⁻⁷ m.
In nanometres: 589 nm. In ångströms: 5.89 × 10⁻⁷ ÷ 10⁻¹⁰ = 5,890 Å.
Photon energy, using hc ≈ 1,240 eV nm: E = 1,240 ÷ 589 ≈ 2.11 eV.
Common mistakes to avoid:
Treating 1 Å as 1 nm. It is one tenth of a nanometre, so 589 nm is 5,890 Å, not 589 Å.
Leaving d in millimetres. Convert to metres before calculating.
Forgetting the order m. In second order, λ = d sin θ / 2 for the same angle.
For more practice with line spectra, our guide to hydrogen spectrum problems works through the Rydberg formula.
What can a student take from Ångström's way of working?
Ångström built his main result in steps over 15 years, each memoir improving on the one before. The obituary also notes a regret: in his last years he was so busy with university administration that his research slowed. Protecting time for careful work mattered then and still does.
If the link between emission and absorption lines feels abstract, the Fermi Simulation Lab has interactive simulations for ideas that are easier to see than read.
Next step: convert three wavelengths from your physics book into ångströms and back into metres, checking each power of ten.
