Hydrogen atom spectrum

The differences between energies of the excited states of the hydrogen atom determine the possible wavelengths, or alternately the frequencies, of photons emitted when excited electrons drop to lower energy states. The set of possible photon wavelengths is called the hydrogen atom spectrum.

This diagram depicts the hydrogen atom spectrum. In the Bohr model of the hydrogen atom, electron energies are represented by orbits around the nucleus.

 

A  hydrogen atom is the simplest atom. Its nucleus consists of one proton, and it has one electron bound to the nucleus. The electron normally exists in its lowest energy state, called the ground state. The ground state is defined as 0 electron Volts, or eV. The energy difference between the ground state and first excited state is 10.2 eV.

 

If the electron absorbs a photon, the energy of the photon goes into raising the electron to an excited state. The excited states of the electron are quantized, that is, only certain energy levels are allowed.

 

If a photon with a wavelength of 121.6 nm, and consequently, an energy of 10.2 eV interacts with an electron in a hydrogen atom, it will be absorbed by the electron, raising the electron to the first excited state. If a 102.6 nm photon (with energy 12.1 eV) is incident on the electron, it will raise the electron to the second excited state. Since electron excited states are quantized, they electrons cannot be excited to energies between these states. For example, a photon with an energy of 11 eV will not excite a ground state electron in a hydrogen atom.

 

If the electron absorbs more energy than is shown in the diagram, it leaves the nucleus, ionizing the atom.

 

The Lyman series of the hydrogen spectrum is a series of transitions where the electron is raised to an excited state and drops directly to the ground state. The photons emitted in these events have high enough energies that they are not visible, they lie in the ultraviolet region of the electromagnetic spectrum.

 

An electron may not drop all the way to the ground state; it might take intermediate steps in-between. In the Balmer series, the electron drops to the first excited state from a higher excited state. The photons emitted from these drops have wavelengths that put them in the range of visible light.

Please watch the Hydrogen Atom Energies Tutorial for an explanation of the photons produced by electrons changing energy levels in a hydrogen atom.

Please go to the interactive simulation at phet.colorado.edu/en/simulation/legacy/hydrogen-atom and run this simulation to get a visual representation of how the Bohr model of the hydrogen atom works. Switch the dial from experiment to prediction, select the Bohr model, and select "Show spectrometer." Click on the light to send photons into the box of hydrogen. As the photons pass through the hydrogen gas, only photons with the right color (wavelength) will interact with the electron. Slow down the simulation and carefully watch what happens. When a photon is absorbed, the electron leaves the smallest ring (ground state) and moves to a larger ring (excited state). After a short time, the electron drops to a lower state and emits a photon. You can see the photon moving sideways.

 

As it jumps to excited states and drops back down, the emitted photons are counted in the spectrometer. Notice the the bigger the jump in energy states, the higher the energy of the photon. In the spectrometer it shows up farther left, with a shorter wavelength.

 

Speed up the simulation and run it for a few minutes to get enough of an emission spectrum to clearly see the Balmer lines, or the specific wavelengths of the emitted photons. Notice that they do not fill in other wavelengths. For example, you do not see 600 nm wavelength photons produced.

 

Feel free to experiment with the other atomic models.

 

This simulation from the University of Nebraska-Lincoln allows you to experiment with photons of varying wavelengths and excited states of the electron. Try to raise an electron to the first excited state, or ionize it completely.

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Of course, stars are made of more than just hydrogen. The spectrum from a star, or from a galaxy full of stars, can give a very good account of the elements present in the star. To analyze the spectrum of our sun, as seen in the above data, the spectral signature has been widened way out to see the details of the absorption lines. The above spectrum was obtained by the National Optical Astronomy Observatory at Kitt Peak in the Arizona desert. It has 50 slices stacked up to show the entire spectrum at once. The solar spectrum is an absorption spectrum. It might seem at first that it should be an emission spectrum, since the light is emitted from the core of the sun. However, the photons pass through the outer layers of the sun before they continue on to earth. The core of the sun is hot, about 15 million K, while the outer layers of the sun are only about 5000 K.

 

The strength of a spectral line depends on how many photons are present (or missing, in the case of an absorption spectrum) and gives an indication of how much of the gas is present. The temperature is also a very important factor. If the gas is very hot, the atoms become ionized. In the case of hydrogen, this means that there are no bound electrons to even raise to excited stated and emit photons. The strength of the lines can give us a good idea of the abundance of electrons raised to an excited state, and thus, a measure of how hot the star is.

 Observational astronomers have become very good at analyzing starlight, and recognizing patterns in the lines. The know about where to look for key identifying lines, like the Ha line. This is the line that corresponds to a hydrogen electron dropping from the third excited state to the second excited state. The observed frequency of the Ha line can be Doppler shifted if the star or galaxy is moving toward or away from us. The amount of the Doppler shift can give us a way to calculate the velocity of the star or galaxy. The figure above shows Doppler shifted spectra. The spectrum in the center is from hydrogen gas that is at rest, and is used as a reference for the other spectra. If the lines are shifted left, their wavelengths are longer, and frequencies lower, indicating relative motion away from the observer. The opposite is true when the object is moving toward the observer.

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If a star or galaxy is rotating, the Doppler shifting broadens the line. The above data shows the effects of broadening on a spectral line due to increasing rotational velocity, from a speed of 15 km/s to 210 km/s.

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The above image shows the effect of pressure broadening on spectral lines. In this sequence, the spectrum on the top is data from low pressure gas, with pressure increasing for the lower samples. When a gas is at high pressure the atoms are colliding with each other with high speeds. The electron orbitals can become distorted in shape, resulting in a spread of emitted photon frequencies.

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We have come a long way in our understanding of atoms and their constituent parts since the Bohr model was developed in 1913. We now know that electrons are not little dots, like planets orbiting a star. Electrons have particle/wave nature and can be best described as a probability function. That is to say, their wavelike properties mean that they are spread out over space like a cloud. The excited states of electrons take configurations like those shown above.

 Observational astronomers have become very good at analyzing starlight, and recognizing patterns in the lines. The know about where to look for key identifying lines, like the Ha line. This is the line that corresponds to a hydrogen electron dropping from the third excited state to the second excited state. The observed frequency of the Ha line can be Doppler shifted if the star or galaxy is moving toward or away from us. The amount of the Doppler shift can give us a way to calculate the velocity of the star or galaxy. The figure above shows Doppler shifted spectra. The spectrum in the center is from hydrogen gas that is at rest, and is used as a reference for the other spectra. If the lines are shifted left, their wavelengths are longer, and frequencies lower, indicating relative motion away from the observer. The opposite is true when the object is moving toward the observer.

 

Observational astronomers have become very good at analyzing starlight, and recognizing patterns in the lines. The know about where to look for key identifying lines, like the Ha line. This is the line that corresponds to a hydrogen electron dropping from the third excited state to the second excited state. The observed frequency of the Ha line can be Doppler shifted if the star or galaxy is moving toward or away from us. The amount of the Doppler shift can give us a way to calculate the velocity of the star or galaxy. The figure above shows Doppler shifted spectra. The spectrum in the center is from hydrogen gas that is at rest, and is used as a reference for the other spectra. If the lines are shifted left, their wavelengths are longer, and frequencies lower, indicating relative motion away from the observer. The opposite is true when the object is moving toward the observer.