Formation of Spectral Lines
Electrons are found surrounding the atomic nucleus at quantized energy levels—sometimes called shells or orbitals. There are an infinite number of energy levels that are separated by smaller and smaller energies as the level number n approaches infinity. The exact separation of the energy levels is determined by the mutual electrostatic repulsion between electrons and the electrostatic attraction between the nucleus and an electron. Gravitational attraction is negligible at the atomic scale (for example, if a hydrogen atom were enlarged to the size of a football stadium, the electron would be nearly invisible orbiting at the top of the bleachers while the proton would be grape seed sized object at the middle of the football field.)
An electron can "jump" to a higher energy level if it absorbs precisely the amount of energy that separates the two levels. Likewise, an electron can emit energy precisely equal to the energy between two levels and cascade down to that lower energy level. If an electron starts from and returns to the same energy level, the energy absorbed exactly equals the energy emitted. The requirement that the energy lost or gained by the electron be equal to the energy difference between levels gives rise to the quantized nature of atomic behavior.
For example, an electron in a hydrogen atom may jump from the n = 1 level to the n = 2 level if the electron absorbs precisely 10.19 eV (electron-volts) of energy. In 1900, the physicist Max Planck determined a relationship between energy E and wavelength λ expressed as
E = hc/λ
where h is a constant of proportionality called Planck’s constant—equal to 6.626 x 10-34 J sec—and c is the speed of light. Note that the inverse relationship between E and λ means that shorter wavelength electromagnetic radiation has higher energy.
In the case of the hydrogen atom, electron transitions that start and stop at the n=2 level result in absorption or emission of energy at wavelengths visible to the eye (see table below).
Line |
Transition |
Wavelength (Å) |
Color |
|---|---|---|---|
Hα |
n=2 «—» n=3 |
6,563 |
crimson red |
Hβ |
n=2 «—» n=4 |
4,861 |
teal green |
Hγ |
n=2 «—» n=5 |
4,341 |
cobalt blue |
Hδ |
n=2 «—» n=6 |
4,102 |
indigo |
The colors seen are very subjective, but the wavelengths observed are unique to the neutral hydrogen atom. Even when red is seen in the spectrum of another element, such as in helium, the exact wavelength will be different from that in hydrogen even if the color may look the same. The structure of the hydrogen atom is depicted below:
Stellar Spectra
Since the absorption and emission steps are but two parts
of a cycle, both steps can be observed, but surrounding conditions will
determine which step is seen (please refer to the discussion of Kirchhoff's
laws of spectroscopy.) If a cloud of gas is observed against a darker/cooler
background, an emission line spectrum is observed (e.g., the Orion
nebula). If a cloud of gas is seen against a hotter/brighter background,
an absorption line spectrum is seen (e.g., the spectrum of a star).
A star’s
absorption spectrum is produced in its lowest atmospheric layer called
the photosphere. What we might simply call its “surface” although
the photosphere is typically several hundred miles thick and is not solid.
The absorption spectrum of hydrogen was used to create the spectral classification scheme OBAFGKM because hydrogen makes up about 75% of all stars’ photospheres and it was most prominent using the limited technology of the time period. Today, high resolution spectra reveal spectral absorption lines due to trace amounts of dozens of other elements and in some case, molecules.
Because of their different electron structures, each element exhibits its spectral signature over a specific temperature range (It may help to recall that temperature is simply a measure of the average kinetic energy of atoms in a gas). Additionally, the temperature of stellar photospheres range from 50,000 K or more to a much "cooler" 3,000 K. Still, even the coolest star is very hot by earthly standards. The strength of a spectral line in a gas depends on the abundance—the number of atoms present—and on the fraction of those atoms which are in the correct state to produce the lines in question. When this fraction is calculated for a range of temperatures and plotted, the curve shows how the strength of the line in the spectrum of the gas varies as the temperature of the gas increases. It is possible to see when the spectral line first becomes visible, reaches its greatest strength, and disappears. An example is shown below:
In the figure, the spectral line strengths of neutral hydrogen (H) and helium (He) are shown, as are the line strengths of ionized calcium (Ca+ or CaII), ionized helium (He+ or HeII), ionized iron (Fe+ or FeII) and the molecule titanium oxide (TiO).
Note that the spectral types are identified by the types O5, B0, A0, etc. since each spectral type can be subdivided into 10 categories from 0 (hotter) through 9 (cooler). Thus, we have B0, B1, ... B9, A0, A1,... A9, F0, etc. and our sun is observed to be a type G2 star.