Much of the information you get about the universe comes from electromagnetic radiation, or light, that you receive from distant reaches in the universe. It is by analyzing that light that you can determine the composition of nebulae, for example. The information obtained from this electromagnetic radiation comes in the form of spectra, or light patterns.
These patterns are formed because of quantum mechanics, which dictates that electrons orbiting atoms can only have specific energies. This concept can be understood using the Bohr model of the atom, which depicts the atom as electrons orbiting around a central nucleus at very specific energy levels.
Electromagnetic Radiation and Photons
In atoms, electrons can only have discrete energy values, and the particular set of possible energy values is unique to each atomic element. Electrons can move up and down in energy level by absorbing or emitting a photon of a very specific wavelength (corresponding to a specific amount of energy equal to the energy difference between the levels).
As a result, elements can be identified by distinct spectral lines, where the lines occur at the wavelengths corresponding to the energy differences between the element's atomic energy levels. The pattern of spectral lines is unique for each element, which means spectra are an effective way of identifying elements, especially from a long distance or in very small amounts.
Absorption spectra are obtained by bombarding an element with light of many wavelengths and detecting which wavelengths are absorbed. Emission spectra are obtained by heating the element to force the electrons into excited states, and then detecting which wavelengths of light are emitted as the electrons fall back down into lower energy states. These spectra will often be the inverse of each other.
Spectroscopy is how astronomers identify elements in astronomical objects, such as nebulae, stars, planets and planetary atmospheres. The spectra can also tell astronomers how quickly an astronomical object is moving away or toward Earth, and by how much the spectrum of a certain element is red- or blue-shifted. (This shifting of the spectrum is due to the Doppler effect.)
To find the wavelength or frequency of a photon emitted or absorbed through an electron energy level transition, first calculate the difference in energy between the two energy levels: ΔE = -13.6eV(1/nf2 - 1/ni2). This energy difference can then be used in the equation for photon energy, ΔE = hf = hc/λ, where h is Planck's constant, f is the frequency, and λ is the wavelength of the photon being emitted or absorbed, and c is the speed of light.
When a continuous spectrum is incident on a cool (low-energy) gas, the atoms in that gas will absorb specific wavelengths of light characteristic of their composition.
By taking the light that leaves the gas and using a spectrograph to separate it into a spectrum of wavelengths, dark absorption lines will appear, which are lines where light of that wavelength was not detected. This creates an absorption spectrum.
The exact placing of those lines is characteristic of the atomic and molecular composition of the gas. Scientists can read the lines like a bar code telling them what the gas is composed of.
A hot gas, in contrast, is composed of atoms and molecules in an excited state. The electrons in the atoms of this gas will jump to lower energy states as the gas radiates away its excess energy. In doing so, very specific wavelengths of light are released.
By taking this light and using spectroscopy to separate it into a spectrum of wavelengths, bright emission lines will appear only at the specific wavelengths corresponding to the photons emitted when the electrons jumped to lower energy states. This creates an emission spectrum.
Just as with the absorption spectra, the exact placing of those lines is characteristic of the atomic and molecular composition of the gas. Scientists can read the lines like a bar code telling them what the gas is composed of. Also, the characteristic wavelengths are the same for both types of spectra. The dark lines in the absorption spectrum will lie in the same places as the emission lines in the emission spectrum.
Kirchoff's Laws of Spectral Analysis
In 1859, Gustav Kirchoff summarized spectra in three succinct rules:
Kirchoff's First Law: a luminous solid, liquid or high-density gas produces a continuous spectrum. This means it emits light of all wavelengths. An ideal example of this is called a blackbody.
Kirchoff's Second Law: A hot low-density gas produces an emission-line spectrum.
Kirchoff's Third Law: A continuous spectrum source viewed through a cool low-density gas produces an absorption-line spectrum.
If an object is at a temperature above absolute zero, it emits radiation. A blackbody is the theoretical ideal object that absorbs all wavelengths of light and emits all wavelengths of light. It will emit different wavelengths of light at different intensities, and the distribution of intensities is called the blackbody spectrum. This spectrum depends only on the temperature of the blackbody.
Photons of different wavelengths have different energies. For a blackbody spectrum to have a high intensity emission of a certain wavelength means that it emits photons of that particular energy at a high rate. This rate is also called the flux. The flux of all wavelengths will increase as the temperature of the blackbody increases.
It is often convenient for astronomers to model stars as blackbodies. Although this is not always accurate, it often provides a good estimate of the temperature of the star by observing at what wavelength the star's blackbody spectrum peaks (the wavelength of light that is emitted with the highest intensity).
The peak of a blackbody spectrum decreases in wavelength as the temperature of the blackbody increases. This is known as Wien's Displacement Law.
Another important relation for blackbodies is the Stefan-Boltzmann Law, which states that the total energy emitted by a blackbody is proportional to its absolute temperature taken to the fourth power: E ∝ T4.
Hydrogen Emission and Absorption Series
The lines in hydrogen's spectrum are often divided into "series" based on what the lower energy level in their transition is.
The Lyman series is the series of transitions to or from the lowest energy state, or ground state. The photons corresponding to these transitions tend to have wavelengths in the ultraviolet part of the spectrum.
The Balmer series is the series of transitions to or from the first excited state, one level above the ground state. (It does not, however, count the transition between ground state and first excited state, as that transition is part of the Lyman series.) The photons corresponding to these transitions tend to have wavelengths in the visible part of the spectrum.
Transitions to or from the second excited state are called the Paschen series, and transitions to or from the third excited state are called the Brackett series. These series are very important for astronomical research, as hydrogen is the most common element in the universe. It is also the primary element that makes up stars.