Video Transcript
Which of the following most
correctly describes the quality of the active medium of a laser that is relevant to
its ability to produce lasing? (A) An active medium contains
completely ionized atoms. (B) An active medium contains atoms
with unstable nuclei. (C) An active medium contains atoms
in which electrons tend to transition to excited states at the same rate that they
tend to transition to relaxed states. (D) An active medium contains atoms
in which electrons tend to transition to excited states at a greater rate than they
tend to transition to relaxed states. (E) An active medium contains atoms
in which electrons tend to transition to relaxed states at a greater rate than they
tend to transition to excited states.
Okay, so this question is all about
what’s called the active medium of a laser. A laser’s active medium could be a
solid, like this here, or a liquid or even a gas. But in any case, the material of
the active medium is carefully chosen to enable lasing. In our various answer options, we
see that some of them refer to what are called excited states as well as relaxed
states. These states have to do with the
particular energy level structure of the atoms that make up the active medium.
Let’s say that we represent those
energy states this way. We can let this line here represent
the ground-state energy level of the atoms in our active medium. We’ll call this level 𝐸 sub g for
the energy of that ground state. And then, let’s say that this
thicker line right here represents all of the excited states of our atom
together. So, we’re grouping our atoms’
excited states all together, and we’re saying that they have an energy called 𝐸 sub
e. Now, when it comes to electrons in
this system, we know that an electron can either occupy the ground state — this, by
the way, is where electrons naturally tend — or if some energy was added into the
system, then an electron could be bumped up to an excited energy level.
Now, another name for a ground
energy level is a relaxed energy level or a relaxed state. So if an electron moves up like
this, we say that it’s excited. And if an electron moves from an
excited state to the ground state, we say it has relaxed. So that’s the meaning of these
terms “excited states” and “relaxed states” that appear in some of our answer
options. So that we can see all five of our
answer options on the same screen, let’s paraphrase the ones we saw on the previous
screen. Those were answer options (C), (B),
and (A).
Answer option (C) is very similar
to options (D) and (E), except (C) says that an active medium contains atoms in
which electrons tend to transition to relaxed states at the same rate of transition
at which they move into excited states. So, note that option (D) says that
transitions to excited states happen at a greater rate than those to relaxed states,
while (E) has the opposite. It says transitions to relaxed
states occur at a greater rate than those to excited states. And then, as we saw, (C) describes
a rate of transition to relaxed and excited states which is the same. So that was answer option (C).
Answer option (B) said that the
active medium of a laser contains atoms with unstable nuclei. And then the very first answer
option, (A), said that the active medium of a laser contains completely ionized
atoms. Now that we’ve got all of these on
the same screen, let’s return to our sketch of these energy levels in the atoms that
make up the active medium.
Recall that we’re looking to
identify the quality of the active medium that relates directly to its ability to
lase. In order for that to happen, we
know that stimulated emission must take place. This involves an electron in an
excited energy level interacting with an incoming photon. If the frequency, in other words,
the energy of this photon, is just right, this interaction can stimulate the
electron to return to a relaxed state and, in the process, to emit a photon with an
identical frequency, phase, and direction as the original one. This process, repeated many times,
produces a beam of coherent radiation characteristic of laser light.
We see then that for lasing to
happen, electrons in the active medium must be in an excited state. If they weren’t — if they were
instead in the ground state like here — then when a photon of just the right
frequency came along, instead of stimulating the emission of another identical
photon, this photon would simply be absorbed and then propel the electron to an
excited state. When electrons are in an excited
state then, they can be stimulated to emit a photon. And this emitted photon adds to the
original one, whereas, on the other hand, if electrons are in the ground state and
they absorb a photon, there’s a net loss of photons one photon in that process. All this to say, for lasing to
occur, there needs to be what is called a population inversion. This is where the number of
electrons in excited states outnumber the electrons in the ground state.
Knowing this, we can start to
eliminate a few of our answer options. First, considering options (A) and
(B), a completely ionized atom has no bound electrons, but it’s just those
transitions made by bound electrons that we need for lasing. Completely ionized atoms, then, are
incapable of supplying the active medium of a laser. So, we’ll eliminate option (A). Option (B) talks about unstable
nuclei in our active medium. This description would indicate
impending nuclear decay in radioactivity. But these processes do not
contribute to the production of laser light. There’s no need for the atoms in
our active medium to have unstable nuclei. And in fact, we’d rather they
not. We’ll cross option (B) off our list
too.
As we consider the remaining three
options, we can see that they’re very similar to one another. All of them describe a transition
rate to excited states and relaxed states and compares those rates. To figure out which of these three
is the best answer, here’s the question we can ask. Which of the three different types
of rates described in these answer options will lead to a majority of electrons in
our atom being in an excited state compared to the ground state? With that question in mind, let’s
look again at answer option (C).
This says that the rate at which
electrons in our atom transition to an excited state is the same as the rate with
which they transition to a relaxed state. If that happened, though, we would
expect there to be the same number of excited electrons as relaxed ones. And this would mean we haven’t
achieved a population inversion. A photon incident on this atom
would be just as likely to be absorbed as it would be to stimulate the emission of
another photon. So when these rates are the same,
as option (C) claims, we won’t be able to amplify the light being produced by
stimulated emission. So, we’ll cross off this
option.
Next, option (E) says that the rate
at which electrons in the atom transition to relaxed states is greater than the rate
at which they transition to excited ones. If that were so, we would expect
our atomic system to look like this, with no excited electrons. But no excited electrons means no
stimulated emission. So, laser light can’t be produced
that way. We’ll cross off this choice
too.
Finally, option (D) says that the
rate at which electrons transition to excited states is greater than the rate at
which they move to relaxed states. Of all our answer options, this is
the only one that would lead to a true population inversion. This would then enable the
production of laser light. So, an active medium contains
atoms, in which electrons tend to transition to excited states at a greater rate
than they tend to transition to relaxed states.
