# Question Video: Identifying the Energy Level Structure of a Laser’s Active Medium Physics

Which of the following diagrams most correctly represents the structure of the electron energy levels in the atoms of the active medium of a laser? [A] Diagram A [B] Diagram B [C] Diagram C [D] Diagram D

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### Video Transcript

Which of the following diagrams most correctly represents the structure of the electron energy levels in the atoms of the active medium of a laser?

Of our four answer options, the first two (A) and (B) show us electron energy levels with three energy states. Both of these answer choices have a metastable state, an excited state, and a ground state. In contrast, answer options (C) and (D) show us electron energy levels with just two states. In option (C), we have an excited state and a ground state and in option (D), a metastable state and a ground state.

One of these four most correctly represents the electron energy levels in the atoms of the active medium of a laser. That bit of information is important because it tells us that the electrons in these energy levels must achieve something called a population inversion. A population inversion occurs when there are more electrons in an energy level above the ground state than there are in the ground state. We call this an inversion because energetically electrons tend toward the ground state.

As we evaluate our answer options, let’s consider those options that have just two energy levels first. Considering answer option (C), let’s imagine that we have some electrons in the ground state of this atom. This is a natural start point because as we mentioned, electrons tend toward the ground state, the lowest energy level. The only way an electron can leave the ground state is if it’s somehow energized, for example, if it absorbs a photon with just the right amount of energy so that the electron is transferred up to an excited state.

In this two-level system, once an electron is in the excited state, it can either remain there or it can decay back down to the ground state. Over even very short time scales, it turns out that it’s much more likely for that spontaneous decay down to the ground state to happen. In other words, electrons tend not to stay in excited states for very long at all. Even though this electron was just elevated to the excited state then, it’s likely to quickly return to the ground state. And this tendency, which is followed by all electrons in the ground state, makes it very unlikely that a population inversion will occur. A two-level system then, with a ground state and an excited state, is an unlikely setup for the active medium of a laser.

Looking next at answer option (D), we see that this option also has two energy levels. However, the elevated energy level is called a metastable state. That name means that if we had a number of electrons in the ground state of this atom and one of those electrons absorbed a photon with just the right frequency, that electron would be elevated to the metastable state and it would tend to stay there. In this way, a metastable state is different from other excited states. If we can get electrons to stay in this energy level, this metastable state, then that seems very promising for achieving a population inversion.

There is one thing we’ll want to keep in mind though. When a photon is incident on our atom with just the right amount of energy to be able to elevate an electron from the ground to the metastable state, that means that photon also has just the right amount of energy to stimulate the decay of this electron back down to the ground state. During that decay, the electron will emit a photon identical to the one that stimulated this emission. This then is a problem in achieving a population inversion. An incoming photon that can lift an electron from the ground to the metastable state is also capable of bringing an electron down from that metastable state. For this reason, the two-level setup that we see in answer option (D) is not a viable option for achieving a population inversion and thereby creating a laser.

Looking next at answer choice (A), we see that this shows us a three-level system. If we once again imagine a number of electrons in the ground state, there’s now the possibility that an incoming photon will elevate a ground state electron to the excited state or that an incoming photon, one with higher energy, will elevate a ground state electron to the metastable state. Once we get to this point though, we start to see some of the same issues that came up in answer options (C) and (D). That is, our excited state electron is unlikely to stay at this level for long.

It’s probable rather that it will quickly decay back down to the ground state, when it comes to electrons in the metastable state, just like before. If an incident photon has the right amount of energy to elevate a ground state electron to the metastable state, then it also has the right amount of energy to stimulate the decay of a metastable state electron to the ground state.

With this three-level system though, we might wonder, if we do have one electron in the excited state and one in the metastable state, isn’t it possible that photons with the right energy will be incident on this atom so as to elevate electrons from the excited into the metastable state? And it is possible for this to happen. As we saw earlier though, electrons in the excited state tend to very rapidly decay back down. This means it’s much more likely that an excited state electron will decay back down to the ground state than it is to absorb a photon and be elevated to the metastable state. Even with these three levels, it’s unlikely for this system to ever create a population inversion and allow lasing.

But now let’s look at answer choice (B). We once again have three energy levels, but now the excited state is at a higher energy than the metastable state. To see how this makes a difference, let’s again imagine we have electrons in the ground state of this atom. If one of these electrons were to absorb a photon that sends it to the metastable state, we would run into the same issue as before, where photons with this particular amount of energy could be absorbed and then elevate an electron from the ground state to the metastable state. But they could also stimulate the decay of a metastable state electron down to the ground state. This particular pathway then will not create the population inversion that we need.

However, if we instead have a photon incident on a ground state electron that has enough energy to excite that electron up to the excited state, that can work in our favor because this excited state electron we know will quickly decay back down to a lower energy level. But in this case, that most accessible energy level is the metastable state. The electron will have a relatively long lifetime in this state. And if we continue to use photons that have that particular energy that elevates electrons from the ground to the excited state, then we won’t run into the problem of driving electrons out of the metastable state into the ground state by accident. Instead, we create a reliable system for populating the metastable state.

Using this approach then, we can achieve a population inversion. This is the necessary condition for lasing. And so, it’s answer option (B) that most correctly represents the structure of the electron energy levels in the atoms of the active medium of a laser.