Absorption Spectra

Atoms do not only emit photons; they also absorb photons. If a photon hits an atom and the energy of the photon is the same as the gap between two electron energy levels in the atom, then the electron in the lower energy level can absorb the photon and jump up to the higher energy level. If the photon energy does not correspond to the difference between two energy levels then the photon will not be absorbed (it can still be scattered).

Using this effect, if we have a source of photons of various energies we can obtain the absorption spectra for different materials. To get an absorption spectrum, just shine white light on a sample of the material that you are interested in. White light is made up of all the different wavelengths of visible light put together. In the absorption spectrum there will be gaps. The gaps correspond to energies (wavelengths) for which there is a corresponding difference in energy levels for the particular element.

The absorbed photons show up as black lines because the photons of these wavelengths have been absorbed and do not show up. Because of this, the absorption spectrum is the exact inverse of the emission spectrum. Look at the two figures below. In the first figure below, you can see the line emission spectrum of hydrogen. The second figure below shows the absorption spectrum. It is the exact opposite of the emission spectrum! Both emission and absorption techniques can be used to get the same information about the energy levels of an atom.

Emission spectrum of Hydrogen.

Absorption spectrum of Hydrogen.

The dark lines correspond to the frequencies of light that have been absorbed by the gas. As the photons of light are absorbed by electrons, the electrons move into higher energy levels. This is the opposite process of emission.

The dark lines, absorption lines, correspond to the frequencies of the emission spectrum of the same element. The amount of energy absorbed by the electron to move into a higher level is the same as the amount of energy released when returning to the original energy level.

Example: Absorption

Question

I have an unknown gas in a glass container. I shine a bright white light through one side of the container and measure the spectrum of transmitted light. I notice that there is a black line (absorption line) in the middle of the visible red band at \(\text{642}\) \(\text{nm}\). I have a hunch that the gas might be hydrogen. If I am correct, between which 2 energy levels does this transition occur? (Hint: look at the figure below and the transitions which are in the visible part of the spectrum.)

Step 1: What is given and what needs to be done?

We have an absorption line at \(\text{642}\) \(\text{nm}\). This means that the substance in the glass container absorbed photons with a wavelength of 642 nm.We need to calculate which 2 energy levels of hydrogen this transition would correspond to. Therefore we need to know what energy the absorbed photons had.

Step 2: Calculate the energy of the absorbed photons

\begin{align*} E& = \frac{hc}{\lambda }\\ & = \frac{\left(\text{6.63} \times \text{10}^{-\text{34}}\right)\times \left(\text{3} \times \text{10}^{\text{8}}\right)}{\text{642} \times \text{10}^{-\text{9}}}\\ & = \text{3.1} \times \text{10}^{-\text{19}}\text{ J} \end{align*}

The absorbed photons had an energy of \(\text{3.1} \times \text{10}^{-\text{19}}\) \(\text{J}\).

Step 3: Find the energy of the transitions resulting in radiation at visible wavelengths

The figure above shows various energy level transitions. The transitions related to visible wavelengths are marked as the transitions beginning or ending on Energy Level 2. Let us find the energy of those transitions and compare with the energy of the absorbed photons we have just calculated.

Energy of transition (absorption) from Energy Level 2 to Energy Level 3:

\begin{align*} \Delta E_{electron} = {E}_{2,3}& = {E}_{2}-{E}_{3}\\ & = \text{16.3} \times \text{10}^{-\text{19}}- \text{19.4} \times \text{10}^{-\text{19}}\\ & = -\text{3.1} \times \text{10}^{-\text{19}}\text{ J} \end{align*}

Therefore the energy of the photon that an electron must absorb to jump from Energy Level 2 to Energy Level 3 is \(\text{3.1} \times \text{10}^{-\text{19}}\) \(\text{J}\).(NOTE: The minus sign means that absorption is occurring.)

This is the same energy as the photons which were absorbed by the gas in the container! Therefore, since the transitions of all elements are unique, we can say that the gas in the container is hydrogen. The transition is absorption of a photon between Energy Level 2 and Energy Level 3.

Important:

The energy of the photon does not correspond to the energy of an energy level, it corresponds to the difference in energy between two energy levels.

Absorption Spectra