Matthew Acevski


I like space. You probably do too. So, I would guess you have probably heard a few things about stars and planets. You may know that the Sun is 75% Hydrogen, 24.9% Helium, and 0.1% other metals. We also know that Mars’ atmosphere is 95% Carbon dioxide, 2.6% Nitrogen, 1.9% Argon, etc. We also know that the red super giant, Betelgeuse, is made up of mostly Helium, but also has traces of Carbon, Oxygen, Sodium, Neon, and Iron [1]. Now, as awesome as that is to know, the question must be asked: How do we know? You could probably guess that on Earth we would have a decent idea of what our atmosphere is made up of, but how do we know about the Sun or stars millions of lightyears away?

The answer to that question is Atomic Spectroscopy. This is a concept that has been worked on for nearly 400 years by some of the brightest minds of history. Newton himself realised that a beam of white light could be separated into its individual colours by refracting the ray through a prism. He concluded that light was made up of small, fast travelling particles that he called “corpuscles”. This theory was later disputed by Christian Huygens, who put forward the idea that light behaved as a wave. This theory was based on the empirical observation known as diffraction; when light goes through a small gap, you can observe the light dispersing outwards on the other side.

These disputes later inspired many experiments, mostly wanting to prove Newton right as he was… slightly more popular. In 1786, David Rittenhouse constructed the first, primitive diffraction grating by holding two hairs parallel to each other using a few screws. Over many years, his design would be adapted and improved as both theoretical knowledge and empirical studies evolved. In 1802, William Hyde Wollaston was the first person ever to observe the dark-line-absorption spectrum of the Sun. Now this sounds like an incredibly important discovery for someone you likely have not heard of; this is because a few years later, the credit went to Joseph von Frauenhofer who, in 1814, not only observed the lines, but managed to measure the wavelengths of many of them after inventing the transmission diffraction grating. These absorption lines were later named Frauenhofer lines.

In 1859, probably the most important discovery with regards to atomic spectroscopy was made. It brought together the work of Frauenhofer with that of a discovery made by Thomas Melville in 1752 where a yellow light was observed when salt was exposed to a flame. Gustav Robert Kirchoff and Robert Wilhelm Eberhard von Bunsen noticed that the emission spectrum of light from various elements exposed to a flame matched some of the Frauenhofer lines emitted by the Sun. This led them to conclude that spectral lines are unique to each element [2]. This is atomic spectroscopy, the identification of the composition of substances by the study of their spectral lines. The spectrum of an element is like its own signature which is unique to that element. We can observe these lines from the Sun, planets and even stars at a great distance away, and this lets us identify their atomic makeup.

Atomic spectroscopy is a concept born out of the nature of quantum mechanics. The idea is also based on the concept proposed by Einstein, that light behaves both as a particle and a wave and this was later adapted by Erwin Schrödinger who proposed in 1926, that an electron can be represented as a wave whose behaviour can be described by a wavefunction. When electrons exist in an atom, they are subject to the Coulomb potential of the nucleus and other electrons in the atoms orbit. In the most basic of examples, the hydrogen atom, you have one electron orbiting a single proton, you can describe the electron by the Schrödinger equation:

(1)   \begin{equation*} -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V(\vec{r})\Psi = E \Psi \end{equation*}

where

(2)   \begin{equation*} V(\vec{r}) = -k \frac{Z^2}{r} \end{equation*}

Where V(\vec{r}) is the Coulomb potential and Z is the charge on an electron [3]. When this equation is solved, we find that, because of the boundary conditions on the system, the energy levels at which the electron can exist in are actually discrete! The ground energy for a Hydrogen atoms electron is -13.6eV, which means it would require at least 13.6eV of energy to be put into the atom for there to be enough energy for the electron to escape the electrostatic pull of the nucleus. This becomes exponentially more complicated as you add more electrons and nucleons to the system. However, the concept still holds, meaning there are energy levels at which electrons can exist in all types of atoms.

The discrete levels that an atom can exist in are not only affected by the nucleus but also by a quantity called “spin”, which all electrons have (as a value of ½). This quantity results in energy levels described by equation 1 splitting into smaller “sub-levels” as the spin gives rise to a magnetic moment which adds another interaction we must account for. With more electrons and protons of higher order elements, we can observe lots of weird and unusual pairs of energy levels [4]. Electrons can transition between these energy levels through three different methods: absorption, stimulated emission, and spontaneous emission. The emissions come as a result of the electrons losing energy and therefore dropping in energy levels by a discrete amount and to conserve energy a photon of frequency equivalent to that of the transition is emitted; meaning a light source of a particular element can be identified by their bright fringes through a spectroscope. The opposite is true for absorption where electrons absorb light of a particular frequency to jump energy levels; this will result in dark fringes (Frauenhofer fringes) at wavelengths that are equivalent to that of the photons absorbed.

You can actually do experiments like this yourself to look for the Frauenhofer lines of certain elements. All you need is something that can separate a beam of light into its continuous spectrum, similar to what Newton did with a prism, all you have to do is get light from a particular source aimed at your make-shift spectroscope and you should be able to observe Frauenhofer lines yourself!

In actual research they do it a bit more professionally. Using extremely powerful telescopes, they can take light samples from stars or even galaxies millions of lightyears away and observe the spectrum of light from these interstellar objects [5]. They can then tell what makes up these objects by comparing the absorption spectrum to that of various common elements are seeing if they match, like a fingerprint identifier for an element. The brightness of these lines can then tell us a lot about the proportions of each of the elements.

This technique has helped us describe the world around us in amazing detail and will continue to do so for years to come with advancements in other adapted techniques such as Fourier Spectroscopy. As a concept, atomic spectroscopy has aided in the discovery and practise of quantum mechanics, cosmology, plasma Physics and even stuff outside of Physics, such as forensics and pharmacology. Given this, I believe atomic spectroscopy to be one of the most underappreciated techniques of Physics which deserves far more recognition than it gets.


References

[1] Shekhtman L. Curiosity Rover Serves Scientists a New Mystery: Oxygen [Internet]. NASA. 2021 [cited 28 April 2021]. Available from: https://www.nasa.gov/feature/goddard/2019/with-mars-methane-mystery-unsolved-curiosity-serves-scientists-a-new-one-oxygen

[2] A Timeline of Atomic Spectroscopy [Internet]. Spectroscopy Online. 2021 [cited 28 April 2021]. Available from: https://www.spectroscopyonline.com/view/timeline-atomic-spectroscopy

[3] Freiberger M. Schrödinger’s equation — what is it? [Internet]. plus.maths.org. 2021 [cited 28 April 2021]. Available from: https://plus.maths.org/content/schrodinger-1

[4] Quantum Numbers and Atomic Energy Levels [Internet]. Hyperphysics.phy-astr.gsu.edu. 2021 [cited 28 April 2021]. Available from: http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qnenergy.html

[5] Bartels M. ‘What Stars Are Made Of’ tells the life story of the woman behind a stellar science [Internet]. Space.com. 2021 [cited 28 April 2021]. Available from: https://www.space.com/what-stars-are-made-of-cecilia-payne-gaposchkin-biography-interview.html