Spectral Lines

1. Spectroscopy

In 1802, British natural philosopher William Hyde Wollaston discovered dark lines in Isaac Newton's colour spectrum. These are now known as spectral lines. Wollaston's discovery may have been attributed to flaws in the prism he used to create a spectrum, but he soon saw that they were always in the same place, whatever prism he used[1].

Image of the solar spectrum showing dark lines at specific wavelengths.

Spectral lines in the solar spectrum. Image credit: MaureenV/Phrood/Saperaud/Cepheiden/Public domain.

German optician Joseph von Fraunhofer independently discovered spectral lines in 1814. Fraunhofer mounted a prism in front a small telescope to create a spectroscope. With this new technology, he was able to map over 570 spectral lines, and created the field of study known as spectroscopy[2].

2. Doppler-shifted lines

French natural philosopher Hippolyte Fizeau showed that light is affected by the Doppler effect in 1848[3]. The Doppler effect was discovered by Austrian natural philosopher Christian Doppler in 1842[4]. Doppler showed that the frequency, and hence wavelength, of sound will change, depending on whether it's moving towards you or away from you.

When it's stationary, the wavelength and frequency of an ambulance siren, for example, will be the same in all directions.

The wavelength appears shorter, and the sound higher pitched, as it moves towards you. This is because the ambulance catches up with the waves it emits, and so the space between emissions is shorter.

Animation demonstrating the Doppler effect.

The Doppler effect. Image credit: Charly Whisky/CC-SA.

Animation demonstrating the Doppler effect on light.

The Doppler effect. Image credit: Cool Cosmos/Public domain.

The wavelength appears longer, and the sound lower pitched, if the ambulance is moving away. This is because in the time between emissions, it moves further from the direction of the waves that you hear, and so the space between emissions is longer.

Fizeau found that the Doppler effect causes light to appear more energetic, and therefore bluer, when it is moving towards us, and less energetic, and therefore redder, when it is moving away.

This effect could be seen in the position of spectral lines, and Fizeau showed that the relative velocity of stars could be determined by comparing the position of the lines in their spectra to the position of lines measured in the laboratory.

Image of unshifted, redshifted, and blueshifted spectral lines. In redshifted spectra, the dark lines are closer to the red end of the spectrum, in blueshifted spectra, they are closer to the blue end.

Image credit: Cool Cosmos/Public domain.

American astronomer Edwin Hubble later discovered evidence for the big bang when he showed that almost all galaxies have spectra that are red shifted, and are therefore moving away from us[5].

3. Absorption and emission lines

In the 1860s, German natural philosophers Gustav Kirchhoff and Robert Bunsen showed that spectral lines are caused by different chemical elements absorbing or emitting light at specific energies[6].

The dark lines found in the spectra of stars are absorption lines. These are caused by clouds of gas that absorb some of the star's light before it reaches Earth. These clouds can then emit this light at the same specific energies, creating emission lines.

Diagram showing that a continuous spectrum is created if light comes directly from a star. Absorption lines are created if the light travels from the star and through a cloud. This is because matter in the cloud absorbs some of the light. An emission spectrum is created from light directly emanating from the cloud, where light is only produced at specific wavelengths.

Image credit: modified by Helen Klus, original image by Magnus Manske/Jhausauer/Public domain.

Image of absorption, emission, and continuous spectra. Absorption spectra show spectral lines. Continuous spectra have no lines, and emission spectra are dark, with lines of colour.

Image credit: Magnus Manske/Jhausauer/Public domain.

Kirchhoff and Bunsen determined the energies of lines produced by different elements in the laboratory, and, in 1864, British astronomer William Huggins and Irish-British astronomer Margaret Huggins showed that stars are made of some of these elements, and that they are mostly made of hydrogen[7].

In 1885, Swiss mathematician Johann Balmer discovered an equation linking the energies of all the hydrogen lines in the visible spectrum[8]. Swedish physicist Johannes Rydberg improved upon this equation in 1888[9].

In the 20th century, Danish physicist Niels Bohr's theory of the atom was used to explain why particular elements are associated with particular energies[10].

4. Blackbody radiation

Kirchhoff coined the term 'blackbody' to describe a hypothetical object that emits a continuous spectrum, with no absorption or emission lines[11]. A blackbody absorbs all of the light that hits its surface. This means that it doesn't reflect light and it doesn't let light pass through it.

When a blackbody is cold it is completely black, and as it heats up it remains in thermal equilibrium, emitting light at all wavelengths. There is no such thing as a perfect blackbody, but there are lots of objects that are close, including the filaments of light bulbs, the hob of electric ovens, larva, metals like iron, and stars.

The relationship between a star's energy and temperature was not known until 1879, when Austrian physicist Josef Stefan showed that the total energy emitted by a black body is proportional to its temperature to the power of four[12]. Five years later, Stefan's first PhD student, Austrian physicist Ludwig Boltzmann, explained this using thermodynamics and British natural philosopher James Clerk Maxwell's theory of light[13].

Stefan and Boltzmann were able to work out the temperature of the Sun's surface by comparing it to other blackbodies found on Earth. They estimated that the surface of the Sun is about 5700 Kelvin (about 5430 °C), which is only about 80 °C less than the currently accepted value. They could then calculate how hot other stars are compared to the Sun.

4.1 Wien's law

In 1893, German physicist Wilhelm Wien showed that the peak wavelength of the light emitted by a blackbody only depends on its temperature. As it heats up, a blackbody will move through the spectrum becoming red, orange, yellow, green, and then blue, no matter what it is made of[14].

Plot of wavelength against brightness. Blackbodies form a curve on this plot. The curve moves towards the blue end of the spectrum the hotter the object.

Blackbody curves. Image credit: Ant Beck/CC-SA.

Wien developed his theory by treating light as if it were made of particles. By the end of the century, however, German physicists Heinrich Rubens and Ferdinand Kurlbaum would show that Wien's theory does not apply to infrared light[15][16]. This problem would be solved by German physicist Max Planck and German-Swiss-American physicist Albert Einstein, using early theories of quantum mechanics.

In 1896, Dutch physicist Pieter Zeeman discovered that spectral lines can be split if the light travels through a magnetic field[17], and in 1913, German physicist Johannes Stark[18] and Italian physicist Antonino Lo Surdo[19] showed that spectral lines can also be split by electric fields. These affects would later be explained using a quantum theory of the atom devised by Bohr in 1913, and developed by German physicist Arnold Sommerfeld[20] and British physicist Paul Dirac[21][22] in the 1920s.

5. References

  1. Wollaston, W. H., 1802, 'A method of examining refractive and dispersive powers, by prismatic reflection', Philosophical Transactions of the Royal Society of London, 92, pp.365-380.

  2. Fraunhofer, J., 1817, 'Determination of the Refractive and Dispersive Indices for Differing Types of Glass in Relation to the Perfection of Achromatic Telescopes', Denkschriften der Bayerischen Akademie der Wissenschaften, 5, pp.193-226.

  3. Gregersen, E., 2011, 'The Britannica Guide to Sound and Light', The Rosen Publishing Group.

  4. Doppler, C., 1842, 'Ueber das farbige Licht der Doppelsterne und einiger anderer gestirne des Himmels' ('On the coloured light of the binary stars and some other stars of the heavens'), Proceedings of the Royal Bohemian Society of Sciences, 2, pp.465-482.

  5. Hubble, E., 1929, 'A relation between distance and radial velocity among extra-galactic nebulae', Proceedings of the National Academy of Sciences, 15, pp.168-173.

  6. Kirchhoff, G. and Bunsen, R., 1860, 'Chemical Analysis by Observation of Spectra', Annalen der Physik und der Chemie, 110, pp.161-189.

  7. Huggins, W. and Miller, W. A., 1864, 'On the spectra of some of the fixed stars', Philosophical Transactions of the Royal Society of London, 154, pp.413-435.

  8. Balmer, J. J., 1885, 'Notiz über die Spectrallinien des Wasserstoffs' ('Note on the Spectral lines of hydrogen'), Annalen der Physik, 261, pp.80-87.

  9. Rydberg, J. R., 1890, 'On the structure of the line-spectra of the chemical elements', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 29, pp.331-337.

  10. Bohr, N., 1913, 'On the constitution of atoms and molecules', The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 26, pp.1-25.

  11. Davidson, M. W., 2011, 'Pioneers in Optics: Joseph von Fraunhofer and Gustav Robert Kirchhoff', Microscopy Today, 19, pp.54-56.

  12. Stefan, J., 1879, 'Über die Beziehung zwischen der Wärmestrahlung und der Temperatur' ('On the relationship between thermal radiation and temperature'), Bulletins from the sessions of the Vienna Academy of Sciences, 79, pp.391-428.

  13. Boltzmann, L., 1884, 'Ableitung des Stefan'schen Gesetzes, betreffend die Abhängigkeit der Wärmestrahlung von der Temperatur aus der electromagnetischen Lichttheorie' ('Derivation of Stefan's little law concerning the dependence of thermal radiation on the temperature of the electro-magnetic theory of light'), Annalen der Physik, 258, pp.291-294.

  14. Wien, W., 1893, 'Die obere Grenze der Wellenlängen, welche in der Wärmestrahlung fester Körper vorkommen können; Folgerungen aus dem zweiten Hauptsatz der Wärmetheorie' ('The upper limit of the wavelengths which can occur in a solid body of the heat radiation; Consequences of the second law of thermodynamics'), Annalen der Physik, 285, pp.633-641.

  15. Rubens, H. and Kurlbaum, F., 1900, Sber. Preuss. Akad. Wiss., pp.929.

  16. Planck, M., 1900, 'On the theory of the energy distribution law of the normal spectrum', Verh. Deut. Phys. Ges, 2, pp.237-245.

  17. Zeeman, P., 1897 (1896), 'On the Influence of Magnetism on the Nature of the Light Emitted by a Substance', The Astrophysical Journal, 5, pp.332-347.

  18. Stark, J., 1913, 'Observation of the separation of spectral lines by an electric field', Nature, 92, pp.401.

  19. Lo Surdo, A., 1914, 'Sul fenomeno analogo a quello di Zeeman nel campo elettrico' ('The phenomenon analogous to that of the Zeeman effect for the electric field'), Il Nuovo Cimento, 7, pp.335-337.

  20. Sommerfeld, A., 1920, 'Ein Zahlenmysterium in der Theorie des Zeemaneffektes' ('A number mystery in the theory of the Zeeman effect'), Naturwissenschaften, 8, pp.61-64.

  21. Dirac, P. A. M., 1928, 'The quantum theory of the electron, Part I', Proceedings of the Royal Society of London, Series A, 117, pp.610-624.

  22. Dirac, P. A. M., 1928, 'The quantum theory of the electron, Part II', Proceedings of the Royal Society of London, Series A, 118, pp.351-361.

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