Video Transcript
The diagram below shows an atom
that interacts with two identical photons in a time interval shorter than the
lifetime of the excited state of an electron in the atom. Which of the following more
correctly shows the changes that have occurred just after the interaction between
the atom and the second photon?
So, what this question and all of
its answers are showing us are three distinct time intervals in which different
interactions are occurring or not yet occurring as in the case of 𝑡 zero, which is
before the photons interact with the atom at all. Then, at 𝑡 one, we see that the
first photon has been absorbed into the lone electron, causing the electron to
become excited and transition to a higher energy level. And after this, we have 𝑡 two,
which occurs right after the second photon interacts with the atom, with the exact
interaction being one of these five answers. So let’s look at them starting with
(A).
(A) shows us the atom with the
electron still in the excited state and no photons anywhere, which implies that this
second photon was absorbed into this already excited electron. But for some reason, the electron
stayed in the same energy state and releasing no photons. Because of this, we know that (A)
cannot be correct. This second photon is interacting
and something is occurring, that something being stimulated emission. When an already excited electron
interacts with a photon, like we see here at 𝑡 one, the electron can actually
transition down in energy level, releasing a photon with the same energy and same
direction as the photon that initially caused this stimulation by interacting with
the excited electron. So, since answer (A) does none of
these things, we know it can’t be correct. So let’s see if this occurs in
answer (B).
Since we don’t see any photons in
answer (B), a stimulated emission couldn’t have occurred. What appears to have happened
instead is that this second photon was absorbed into this already excited electron,
causing it to become even more excited and transition up to an even higher energy
level. This process is very much
possible. Very energetic photons can
transition already excited electrons up an energy level, maybe even several at a
time. But this particular transition
cannot occur in this case because this electron is interacting with two photons that
are identical, meaning that they have the same energy.
When this first photon is absorbed
at 𝑡 zero, it causes the electron to jump up from the first energy level, which
we’ll call 𝐸 one, to the second energy level, which we’ll call 𝐸 two. And now, what’s happening in
diagram (B) is that the already excited electron in 𝐸 two absorbs the second
photon, causing a transition upwards to the third energy level, which we’ll call 𝐸
three. This is the general process that’s
occurring, but it’s not something that can actually happen in reality because these
two photons here have identical energies.
And so if the first photon has
enough energy to send the electron from the first to the second energy level, then
the second photon must also have that energy. But higher energy levels have
higher differences in energy, which means it would take more energy to go from 𝐸
two to 𝐸 three, then from 𝐸 one to 𝐸 two. So, the second photon actually
won’t be energetic enough to cause a transition upwards for this electron to the
third energy level, which means that (B) is not the correct answer here since the
second photon does not have a higher energy than the first photon.
So, let’s now turn our attention to
answer (C). At first glance, answer (C) appears
to be showing us a stimulated emission. The second photon stimulates an
already excited electron, causing the electron to emit a photon with the same
direction and energy as the incident photon, which also travels alongside it, since
in stimulated emissions, the incident photon that stimulates the excited electron is
not absorbed. However, this diagram actually is
not showing us a correct stimulated emission because this excited electron has a
transition downwards in order to emit this photon. So, because (C) doesn’t show the
electron in the lower energy level, it can’t be correct. But if we look at diagram (E), we
see that it does show the electron and the lower energy level.
An excited electron interacts with
a photon, causing it to transition down in energy level and emit a photon with the
same energy and same direction as the incident photon. This is what we expect to occur in
a stimulated emission. So answer (E) shows us a stimulated
emission. But how do we actually know that
this is what’s going to occur here? Well, it has to do with what’s said
in the first sentence. The photon interactions are
occurring at a time interval shorter than the lifetime of the excited state of an
electron in the atom. This means that between 𝑡 zero and
𝑡 one, there is no time for the electron that was excited by the first photon to
transition downwards. If this were the case, we would see
something like what occurs in diagram (D), which is an example of spontaneous
emission.
Spontaneous emission occurs when an
excited electron transitions to a lower energy level by itself, releasing a photon,
which has the same energy as the photon that initially excited the electron but a
different direction. Spontaneous emission occurs
spontaneously. Physical systems in general tend
towards the lowest stable energies. So, when there’s an electron in an
excited state, if there is a lower energy state available, then it will decay
downwards to it, releasing a photon in the process. But it still takes time for this
transition downwards to occur usually on time scales of 10 to the power of negative
eight seconds.
So, although spontaneous emission
occurs very quickly, if two photons are able to interact with this same electron
with a time interval shorter than the lifetime of the excited state of an electron,
then it means that a stimulated emission will occur instead since there isn’t enough
time for the excited electron to transition downwards before this second photon
comes in and causes a stimulated emission.
Therefore, the process that most
correctly shows the changes that have occurred just after the interaction between
the atom and this second photon would be stimulated emission, which is shown
correctly in diagram (E).
