Question Video: Describing a Metastable Electron State Physics

Which of the following most correctly describes a metastable state for the energy of an electron in an atom? [A] A metastable electron state is the state in which the electron is not completely ionized but moves more like a free electron than a bound electron. [B] A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which the electron will tend to remain for significantly less time than the typical lifetime of an electron in an excited state. [C] A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which an electron is more likely to absorb photons than in other excited states. [D] A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, which the electron can only transition to by simultaneously absorbing and emitting photons. [E] A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which the electron will tend to remain for significantly longer than the typical lifetime of an electron in an excited state.

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Video Transcript

Which of the following most correctly describes a metastable state for the energy of an electron in an atom? (A) A metastable electron state is the state in which the electron is not completely ionized but moves more like a free electron than a bound electron. (B) A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which the electron will tend to remain for significantly less time than the typical lifetime of an electron in an excited state. (C) A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which an electron is more likely to absorb photons than in other excited states. (D) A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, which the electron can only transition to by simultaneously absorbing and emitting photons. And lastly, (E) a metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which the electron will tend to remain for significantly longer than the typical lifetime of an electron in an excited state.

Recall that our goal is to choose from among five options for the best description of a metastable electron state. We’re not able to fit all five complete answer descriptions on the screen at one time, but we can write shortened versions of the previous four. So we have an easier time evaluating which of the five is best.

In answer option (A), a metastable electron state was claimed to be a state in which an electron is not ionized but rather that it moves more like a free than a bound electron. Answer choice (B) said that a metastable electron state is a state that is higher than the ground state in which an electron remains for less time than it does in a usual excited state. Option (C) described a metastable electron state as one in which an electron is more likely to absorb photons than in other excited states. Lastly, option (D) described a metastable electron state as one to which an electron can only transition by simultaneously absorbing and emitting photons.

These then are our five answer options. As we evaluate them, let’s think of a three-level system that consists of a ground state, an excited state, and a metastable state. This type of system often appears in lasing applications. In such a system, some electrons in the ground state are transitioned to the excited state. The lifetime though of an electron in a typical excited state is fairly short. That electron will tend to decay down, it’s called, to a lower energy state, in this case the metastable state. A metastable state is an excited state in the sense that it is a higher energy level than the ground state. What makes this special though, as the name implies, is that electrons in this state tend not to quickly decay down to lower energy levels. This is the main way that a metastable state is different from a typical excited state.

Knowing this, let’s consider again answer option (B). This option says that a metastable electron state is higher than ground state. And that’s true. But it then goes on to say that an electron in this state remains less time than in a usual excited state. This part of the statement is inaccurate. And so we’ll cancel out option (B) from further consideration.

Option (C) says that in a metastable state, an electron is more likely to absorb photons than in other excited states. However, we know that for an electron in a metastable state, its likelihood of absorbing a photon depends simply on the energy states around it and the photons available. If there is a match between incident photon energy level and the energy gap between the metastable state and some other state in the atom, then that electron will indeed absorb the incident photon. Electrons in metastable states are neither more nor less likely to absorb photons than electrons in other excited states. We’ll cross out answer choice (C).

Answer option (D) says that electrons can only transition to metastable states by simultaneously absorbing and emitting photons. While electrons can transition to metastable states by absorbing or emitting photons, there’s no requirement that this happens at the same time. Rather, an absorption event or an emission event can happen by itself. Answer choice (D) won’t be our answer either.

Option (A) says that electrons in metastable states are not ionized. This means that the electron is still within the various energy levels of an atom. This statement is accurate. But then option (A) goes on to say, “An electron in a metastable state moves more like a free electron than a bound electron.” However, so long as an electron is in a metastable state, it is a bound electron. Therefore, its motion will be more like a bound electron than an electron free to move about between different atoms. We’ll cross out then answer choice (A).

This leaves us with option (E), that a metastable electron state is the state of an electron that is at a higher energy level than the ground state energy of that electron. Based on our sketch, we know that this part of that statement is true. And then option (E) goes on to say, “in which the electron will tend to remain for significantly longer than the typical lifetime of an electron in an excited state.” Indeed, this last part of answer option (E) explains why the state is called a metastable state. Electrons do indeed tend to remain there for significantly longer than they do in other excited states in the atom.

For our final answer then, we choose option (E). A metastable electron state is the state of an electron that is at an energy level higher than the ground state energy of that electron, in which the electron will tend to remain for significantly longer than the typical lifetime of an electron in an excited state.

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