# Hydrogen atom spectrum

We see that different gases have different emission specta, like a fingerprint that can be used to identify the kind of gas emitting the spectral lines. Now we need to understand more about how those spectral lines are made and why they are specific to a gas.

The reason behind why the colored bands have the colors they do has to do with how they are created. We will do this by looking in-depth at one gas: hydrogen. We choose hydrogen because it is a very simple atom. An atom has a nucleus made of protons and neutrons. The number of protons present defines the kind of gas. Hydrogen is a very simple atom, it just has one proton in its nucleus and no neutrons. It also has one electron that is bound to the nucleus.

When a photon of a specific energy interacts with an electron in a hydrogen atom, the electron absorbs the energy of the photon and is raised to an excited state. The electron stays in that excited state for a short time and then drops back down to a lower state.

Only specific excited states exist for an electron in a hydrogen atom. It can absorb only photons that correspond to the energies of its possible excited states. We say that the electron energies are "quantized."

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. The electron normally exists in its lowest energy state, called the ground state. The ground state is defined as 0 electron Volts (eV) and has quantum number n = 1. 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 13.6 eV or more, 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.

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.

## Hydrogen atom electron energies

This graphic illustrates the hydrogen atom energies. The ground state energy is zero electron Volts (eV) while the first, second, third and fourth excited states have energies of 10.2 eV, 12.1 eV, 12.8 eV and 13.1 eV, respectively.

An electron may not drop all the way to the ground state; it might take intermediate steps. For example, there are three ways an electron in the second excited state can drop eventually to ground. It can drop from the second excited state all the way to ground or it can drop in two steps, from the second to first excited state, and then from the first excited state to ground. The drop from the second to first excited state would emit a photon of energy 1.9 eV (12.1 eV - 10.2 eV = 1.9 eV).

Please watch the Hydrogen Atom Energies Tutorial to learn more about photons absorbed and emitted when electrons change energy levels in a hydrogen atom.

# Models of the atom

Our current understanding of atoms has developed over time. Early scientists thought atoms were little balls, like billiard balls. Another early model imagined that atoms were like plum pudding with electrons scattered like raisins in the pudding. The classic solar system model, the Bohr model and the deBroglie model all have salient aspects but break down at some point. The Schroedinger model is a more recent quantum mechanical approach.

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.

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.

The difference of the Doppler shifted wavelength and the wavelength at rest gives us the change in wavelength. The ratio of the change in wavelength to the rest wavelength equals the ratio of the velocity of the star or galaxy to the wave speed. Since the signal is light, the wave speed is the speed of light. We can use this formula to calculate the velocity of the star or galaxy that is emitting light that is red shifted or blue shifted.

If a star or galaxy is rotating, one side is moving toward us and the other side is moving away. The Doppler shifting of the light from both sides broadens the line as seen in the light spectrum curve. The above data shows the effects of broadening on a spectral line due to rotational velocity for four stars, from a speed of 15 km/s to 210 km/s. Notice that the faster the rotation, the broader the line. This means we can analyze light from a star or galaxy to tell how fast it is spinning.

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.

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. The simplest shapes of the electron probability clouds are spherical, but they can also take on mor complicated structure with four-fold symmetry and more.

We cannot see electrons, even with the most sensitive optical microscope. Atoms are about an angstrom in size, which is 10-10 meters. The shortest wavelength of visible light is 400 nanometers, or 4 x 10-7 m. This means that the shortest wavelength visible light is some four thousand times the size of an electron orbital.

The image above shows an atomic scale structure called a quantum corral, imaged by a scanning tunneling microscope (STM). It was created using a STM to pick up and place individual atoms in a circle. The wave structure inside the circle is evidence of the wave nature of electrons.

Please visit the IBM STM image gallery to see more images produced by scanning tunneling microscopes and to learn about how they work.