## Spectral Lines

As discussed on the preceding pages, an atom’s electrons cannot have just any arbitrary energy. The energy of each electron must always fit one of the atom’s orbitals—i.e., one of the wave-like states that the electron is allowed to have as it “orbits” the nucleus. I put “orbits” in quotes here, because the electron isn’t really orbiting the nucleus, at least not in the sense that planets orbit the sun. But it’s doing something analogous to orbiting, somehow, as it pretends to be both a particle and a standing wave. There are several important consequences of this fact. For one, it means that an atom can’t absorb or emit just any amount of energy in the form of light. When an incoming wave of light hits an atom, one of the atom’s electrons may absorb some or all of that energy, jumping to a higher-energy orbital in the process. But if the incoming light wave doesn’t have enough energy to bump the electron up to the next orbital, the electron won’t absorb any energy at all, since its energy must always fit one of the allowed orbitals.

On the other hand, if the incoming light wave has more energy than the electron needs to reach the next orbital, the electron might jump up two or three orbitals at once. In this case, it will absorb precisely the energy it needs to reach that higher orbital. No more, no less.

Conversely, if an electron is already on a high-energy orbital, it may lose energy and fall to a lower orbital by emitting a wave of light. The total energy of the light it emits must be exactly equal to the difference in energy between the high orbital on which the electron began and the low orbital to which it fell. So, whenever an atom emits light, the energy of that light always corresponds to the difference in energy between two of the atom’s orbitals.

These facts about light absorption and emission have important practical implications. As we saw in chapter 2 (here), the energy of a light wave corresponds to its frequency and wavelength, which determine its color. Therefore, the energy of an atom’s lowest orbital can be measured simply by observing what colors of light the atom absorbs. Similarly, the differences in energy between an atom’s various orbitals can be determined by observing what colors of light the atom emits. This is especially useful when trying to determine what chemical elements an object contains. The energies of an atom’s orbitals depend on the type of atom: hydrogen orbitals have different energies than helium orbitals, and so on. This means that each chemical element absorbs and emits light with a unique set of colors! The colors of light that an atom absorbs or emits provide a sort of “fingerprint” by which the type of atom can be identified.

These “atomic fingerprints” are easy to observe, using a device called a spectroscope. A typical spectroscope uses either a prism or a diffraction grating to separate a beam of light into its component colors. The light first goes through a narrow slit, so that after the colors are separated they appear as sharp lines rather than blurring together. These lines of color, called emission lines, tell us what type of atom (or atoms) emitted the light. Conversely, absorption lines correspond to the colors absorbed by atoms when many different colors of light pass through; they appear as dark lines in an otherwise bright color spectrum.

Spectroscopy, the study and analysis of spectral lines (emission lines and absorption lines), is especially useful in astronomy and cosmology. By analyzing spectral lines in the light from stars and galaxies, astronomers can figure out what those distant objects are made of. Analysis of spectral lines also makes it possible to measure Doppler shift in the light from stars and galaxies, allowing astronomers to calculate the speed at which a star or galaxy is moving toward us or away from us. This has led to important discoveries in cosmology, as we’ll see in chapter 8.

Spectroscopy also played a crucial role in the development of quantum mechanics. Spectral lines had been discovered long before Bohr proposed his model of the atom, and one of the greatest successes of the Bohr model was its ability to explain why these lines appear. The model even made it possible to predict exactly what colors of light should be emitted by various types of atoms. Its predictions proved exactly right for hydrogen, but Bohr’s model gave incorrect predictions for the spectral lines of other elements. (That is, it predicted the wrong sets of colors for elements other than hydrogen.) The theory of quantum mechanics soon solved that problem, accurately predicting what colors of light should be emitted by each type of atom. This is one of many impressive triumphs of quantum mechanics. An even greater triumph is its ability to explain chemical properties, as we’ll see in the next section.