# Spectroscopy

By

Ervin Chia

,

Chua Wei Hong

,

Hillson Hung

,

Nemo Chen

●

Published 2022-08-15

We rounded off the section on optics with a very important property of light: diffraction patterns through gratings. By employing diffraction gratings, light of different wavelengths are distributed differently across space. This is instrumental because it allows us to break down incoming light into its constituents; you may think of it as reverse superposition across space. The technique and field of splitting light into different wavelengths and observing its interactions with other matter is known as spectroscopy. A famous and early example of spectroscopy is Newton's prism where Sir Isaac Newton was able to split light from a pinhole into its constituent colours using a glass prism. The image formed as a result of performing spectroscopy is known as a spectrum, detailing the presence of the constituents of the light measured. Over the years, new methods and equipment were developed to split light more effectively and precisely.

Optics and spectroscopy has had a long runway to develop; even in the 1800s, the spectra of all kinds of light sources were investigated. An emission spectra is one type of spectrum, by which an object is allowed to emit light. This light is then collected and split into its constituents. For many sources such as fire, light bulbs and even the sun, a continuous spectrum was observed. However, when elements were heated and allowed to emit or excited through electrical means, scientists observed that their emission spectra were discrete and not continuous. No one was able to explain why, even though many empirical observations and formulae were written. One famous example is the Rydberg formula by Johannes Rydberg:

\begin{align}
\frac{1}{\lambda}=RZ^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)
\end{align}

The Rydberg formula originally describes the relationship between the discrete emission lines observed and their wavelengths. It was eventually found to be extendable to certain specific elements such as sodium and lithium. Discreteness of the emission is captured by number n: these values are only allowed to take integer values, and emissions are described from a higher integer n_{2} to a lower n_{1}.

As heavier elements were investigated, the emission spectra quickly become very complicated; some having very fine differences as well as having many more emissions. Compare the complexity of Hydrogen's spectra to that of Iron:

This then became a huge problem that physicists were unable to solve for a long time: What governed these emissions, and why were they unique to each element? Even after repeating spectroscopy on materials under different conditions such as temperature or pressure, the emission spectra remained the same. As a result, emission spectras of atoms could be used as a elemental "fingerprint": if one had a catalog of individual spectrum of elements, then given an unknown spectrum, one can find what elements are found in the source of the emission! This is known as atomic emission spectroscopy and is highly useful in probing materials at very low quantities. Therefore, despite the puzzling nature of the discreteness of emissions from elements, they were very useful.

Go to Activity 4.

When we have an object made up of a dense collection of particles in motion, the distribution of kinetic energies give rise to a measurable macroscopic quantity called temperature¹. Any object with a non-zero temperature will give out light in the form of blackbody radiation. This form of light has a continuous distribution of wavelengths. The key differences between blackbody radiation and atomic emissions are summarised in the table below.

Earlier, we discussed the successes of the particulate nature of light in the late 1800/early 1900s. The problem faced by Max Planck, known as the ultraviolet catastrophe, is exactly this phenomenon of blackbody radiation. Consequentially, this broad and continuous distribution of radiation emitted by hot objects is known as the Planck distribution. We will not dwell too long with blackbody radiation as we will save the more in-depth discussions on this topic in a later chapter. In the meantime, to get a better understanding of blackbody radiation, Go to Activity 5.

Are there any light emission that is a combination of both blackbody and discrete transitions? Study the spectrum of a galaxy (SDSS object 582093484903825431) below.

Another method to probe a sample's constituent elements is to perform the opposite of an emission spectra: an absorption spectra. As it turns out, just as specific wavelengths of light is emitted by an element, shining light with those same wavelengths will result in absorption; collecting the light that passes through and splitting it is known as an absorption spectra.

A typical setup for absorption spectroscopy is shown below. The sample is illuminated by a broadband light source. Certain wavelengths of light will be absorbed by the sample. The light that paasses through the sample is split by a diffraction grating or prism and the spectrum is collected by photodetectors or a camera for analysis. Absorption spectroscopy is probably the most commonly used spectroscopic technique used in research and industrial labs.

Additionally, spectroscopy has proven exceptionally useful in probing things that are (i) delicate and precious or (ii) hard to access, which categorically encompass many things such as dinosaur fossils, artwork, new materials, and of course celestial objects.

In 1802, the spectrum of our very own star was studied, and was found to have interesting properties and dark fringes. In 1814, Joseph von Fraunhofer studied the wavelengths at which these dark fringes occurred and classified them, giving rise to the eponymous Fraunhofer lines. The Fraunhofer lines give us insight to both the solar and planetary atmospheres, since light from the sun must have interacted with both before reaching the surface of Earth.

In more modern times, one can efficiently collect light from other stellar sources to analyse their spectra. The figure below shows a spectrum of a star (SDSS object 75094094052851712).

Through spectroscopy, we are able to identify what stars are actually made of, and with that, we are able to build an understanding of the cosmos.

In summary, the light being absorbed and emitted by elements encodes information about the atoms themselves. The principle is straightforward, and a wide variety of problems can be solved by this technique. However, at this stage, we are unsure of how the atom is able to accept and emit very specific wavelengths of light. To understand how it does so, we must travel back in time once again to follow the models that tried to explain what the enigmatic atom is.

Go to Activity 6.