Suppose we want to measure the energy difference between the ground state and any one of the excited states. How do we do it? Answer: Spectroscopy! We shine light onto the atoms and look at what happens to the light. In modern spectroscopy, we use laser light. Light, including laser light, is composed of tiny particles known as photons.1 As an analogy, think about a stream of water. The water looks continuous, but it is actually made up of tiny water molecules. The same thing is true with light. Light is composed of tiny particles we call photons. There is, however, a really important difference between water molecules and photons. The energy of a photon is determined only by the frequency of the light wave. The more the light wave oscillates up and down in one second, the larger the energy of an individual photon that makes up that light wave. The energy of a water molecule, on the other hand, is related to how fast the molecule is moving, rotating, and vibrating. We will explore the connection between the frequency of the light wave and the energy of a photon more in the next section.
▶ Important Statement If a photon has the same energy as the energy difference between the ground state and an excited state, the atom will absorb that photon and move an electron to the excited state. If the photon does not have the same energy as that energy difference, the atom will completely ignore the photon.2
Thought Experiment Time Imagine you have an electron behaving like a wave orbiting around a nucleus. That electron wave has to constructively interfere with itself, and we can think about that standing wave as having some amount of energy. Let’s call this energy E1. If we wanted to add another loop to the standing wave, we need to add energy to the system. Suppose an electron with 1 more standing wave loop has energy E2. Remember that the electron needs to be a standing wave, which has a specific energy. If it wasn’t, the electron would experience destructive interference. We want to move an electron from the lower energy standing wave to the higher energy standing wave. How much energy do we need to put into the system? The answer is in the footnotes.3
This is the basic idea behind spectroscopy. If we want to excite an electron from one energy level, which has some energy, to another energy level, which has a different energy, we need to provide the system with the correct difference in energy.
Restating that in terms of an actual experiment: We send a laser through an optically clear container, called a cell or vapor cell, filled with atoms. We will smoothly scan the energy of the photons over time and monitor the transmission of the laser through the cell. If the energy of the photons does not match the energy difference between the ground state and an excited state, the laser light will pass right through the atoms with no losses. If the energy of the photons matches that energy difference, light will be lost from the laser and the transmission will decrease. Experiments that match the above description are known as absorption spectroscopy experiments. We, as experimentalists, simply monitor the transmission of the laser through an atomic sample as we change the photon energy. When the amount of transmitted light drops, we learn what energy is required to excite the atoms from the ground state to an excited state. Believe it or not, that is, conceptually, all there is to it. In the lab things are a bit more complicated, but this is the basic idea. We will finish up this section with a new definition.
1- German physicist Max Planck won the 1918 Nobel Prize in physics for discovery of the photon. Albert Einstein won the 1921 Nobel Prize in physics for explaining the photoelectric effect, which determined that a beam of light is made up of a bunch of photons. I may be biased, but Einstein’s explanation of the photoelectric effect was the most important discovery of the twentieth century.
2- This important statement is super important, but it also isn’t 100% correct. We are going to start with this statement to get at some important concepts. In the next few chapters, we are going to discuss some more physics and then restate this important statement to something more correct. It’s kind of like the flowchart from the beginning of the chapter. We start simple and build up complexity.
3- We would need to add precisely E2 − E1 of energy.
