Discover How We Came to Know the Cosmos

Chapter 7. Spectral Lines

18th December 2017 by Dr Helen Klus

7.1 Spectroscopy

In 1802, British natural philosopher William Hyde Wollaston discovered dark lines in Isaac Newton’s colour spectrum (discussed in Chapter 3). These are now known as spectral lines. Wollaston’s discovery may have been attributed to flaws in the prism he used to create the spectrum, but he soon saw that they were always in the same place, whatever prism he used.[1]

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]

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

Figure 7.1
Image credit

Spectral lines in light from the Sun.

7.2 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.

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.

The Doppler effect.

Figure 7.2
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The Doppler effect.

Fizeau found that the Doppler effect causes light to appear more energetic, and therefore bluer, when it’s moving towards you, and less energetic, and therefore redder, when it’s 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:

Δλ/λ = Δν/ν = v/c (7.1)

Here, λ is the wavelength where the spectral line appears for light from the Sun and Δλ is the change in wavelength between this and the wavelength where the spectral line appears for light from something moving relative to the Sun. v is the velocity at which it’s moving, c is the speed of light, and ν is the frequency.

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] (discussed in Book I).

7.3 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.

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] and 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] (discussed in Chapter 10).

Cool Cosmos Courtesy NASA/JPL-Caltech. Cool Cosmos Image Use Policy.

Figure 7.3
Image credit

Spectral lines shifted due to the Doppler effect.

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.

Figure 7.4
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Continuous, absorption, and emission spectra.

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.

Figure 7.5
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Blackbodies, like stars, produce a continuous spectrum, absorption lines are caused by hot gases that absorb some of this light, and emission lines are caused by hot gases emitting light.

7.4 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 so cannot act as a mirror) and it doesn’t let light pass through it.

When a blackbody is cold it’s completely black, and as it heats up it remains in thermal equilibrium, emitting light at all wavelengths. There’s 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 blackbody 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 knew that:

F = L/4πd2 (7.2)

Here, F is the energy flux - energy per m2 per second, L is the luminosity - energy per second, and 4π2 is the surface area of a sphere, where the distance between the observer and the luminous object (d), is the radius of the sphere.

Diagram of the Sun, showing that flux is equal to luminosity per surface area.

Figure 7.6
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Flux is the luminosity (energy per second) per surface area.

Stefan and Boltzmann showed that at the surface of a blackbody, where d is the radius of the blackbody (r):

F = L/4πr2 = σT4 (7.3)

Here, T is the effective temperature - the temperature assuming it’s a perfect blackbody, and σ is a constant, known as the Stefan-Boltzmann constant.

Stefan and Boltzmann were able to determine the temperature of the Sun’s surface by comparing it to blackbodies on Earth. They estimated that the surface of the Sun is about 5700 Kelvin (about 5427 °C), which is only about 80 Kelvin (80 °C) less than the currently accepted value.

7.4.1 Wien’s law

In 1893, German physicist Wilhelm Wien showed that the peak wavelength of the light emitted by a blackbody (λmax), which determines its colour, only depends on its temperature (T). As it heats up, getting more energetic, the light from a blackbody will decrease in wavelength. It will move through the spectrum becoming red, orange, yellow, green, and then blue, no matter what it’s made of.[14] Once the temperature of stars could be determined from their colour, their radius could be determined using the Stefan-Boltzmann equation.

λmax = 0.0029/T (7.4)

Here λmax is measured in metres and T is measured in Kelvin.

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.

Figure 7.7
Image credit

As a blackbody gets hotter, it emits light with shorter wavelengths, becoming bluer.

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 showed 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 (discussed in Chapter 8).

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 (discussed in Chapter 10), and developed by German physicist Arnold Sommerfeld[20] and British physicist Paul Dirac[21,22] in the 1920s (discussed in Chapter 11 and Chapter 12).

7.5 References

  1. Wollaston, W. H., Philosophical Transactions of the Royal Society of London 1802, 92, 365–380.

  2. Fraunhofer, J., Denkschriften der Bayerischen Akademie der Wissenschaften 1817, 5, 193–226.

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

  4. Doppler, C., Proceedings of the Royal Bohemian Society of Sciences 1842, 2, 465–482.

  5. Hubble, E., Proceedings of the National Academy of Sciences 1929, 15, 168–173.

  6. Kirchhoff, G., Bunsen, R., Annalen der Physik und der Chemie 1860, 110, 161–189.

  7. Huggins, W., Miller, W. A., Philosophical Transactions of the Royal Society of London 1864, 154, 413–435.

  8. Balmer, J. J., Annalen der Physik 1885, 261, 80–87.

  9. Rydberg, J. R., The London Edinburgh and Dublin Philosophical Magazine and Journal of Science 1890, 29, 331–337.

  10. Bohr, N., The London Edinburgh and Dublin Philosophical Magazine and Journal of Science 1913, 26, 1–25.

  11. Davidson, M. W., Microscopy Today 2011, 19, 54–56.

  12. Stefan, J., Bulletins from the sessions of the Vienna Academy of Sciences 1879, 79, 391–428.

  13. Boltzmann, L., Annalen der Physik 1884, 258, 291–294.

  14. Wien, W., Annalen der Physik 1893, 285, 633–641.

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

  16. Planck, M., Verh. Deut. Phys. Ges 1900, 2, 237–245.

  17. Zeeman, P., The Astrophysical Journal 1897 (1896), 5, 332–347.

  18. Stark, J., Nature 1913, 92, 401.

  19. Lo Surdo, A., Il Nuovo Cimento 1913, 7, 335–337.

  20. Sommerfeld, A., Naturwissenschaften 1920, 8, 61–64.

  21. Dirac, P. A. M., Proceedings of the Royal Society of London Series A 1928, 117, 610–624.

  22. Dirac, P. A. M., Proceedings of the Royal Society of London Series A 1928, 118, 351–361.

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How We Came to Know the Cosmos: Light & Matter

I Pre 20th Century theories

1. Atoms and Waves

2. Reflection, Refraction, and Diffraction

3. Newton's theory of Light

4. Measuring the Speed of Light

5. 19th Century Wave Theories

6. 19th Century Particle Theories

7. Spectral Lines

II Quantum Mechanics

8. Origin of Quantum Mechanics

9. Development of Atomic theory

10. Quantum Model of the Atom

11. Sommerfeld's Atom

12. Quantum Spin

13. Superconductors and Superfluids

14. Nuclear Physics

15. De Broglie's Matter Waves

16. Heisenberg's Uncertainty Principle

17. Schrödinger's Wave Equation

18. Quantum Entanglement

19. Schrödinger's Cat

20. Quantum Mechanics and Parallel Worlds

III Quantum field theories

21. The Field Concept in Physics

22. The Electromagnetic Force

23. The Strong Nuclear Force

24. The Weak Nuclear Force

25. Quantum Gravity

IV Theories of the mind

26. Mind-Body Dualism

27. Empiricism and Epistemology

28. Materialism and Conscious Matter

29. Material theories of the Mind

30. Material theories of the Mind vs. Descartes

31. The Mind and Quantum Mechanics

32. The Limitations of Science

V List of symbols

33. List of symbols

34. Image Copyright