Video Transcript
The diagram below shows stimulated
emission of light from an atom. In which of the following ways is
the stimulated emission incorrectly shown? (A) The electron should be in an
excited state. (B) Two photons should be
shown. (C) The emission is shown
correctly.
To determine which of these three
is correct, let’s go through all of the steps of a typical stimulated emission,
starting with an atom that has a single stable electron in the ground state. In order for any type of emission
to occur, this ground state electron must become excited. Typically, this excitation happens
when a photon interacts with the electron. If the energy of this photon is
equal to the difference in energy between the electron energy levels, which for
convenience in this case we’ll show as being between the first and second energy
levels, then the electron can absorb the photon, causing it to transition upwards to
a higher energy level.
When the electron is in this higher
energy level, we say that it is in an excited state. And while it is here, there are one
of two types of emission that can occur: stimulated or spontaneous. Spontaneous emission occurs if the
electron spontaneously decays. This spontaneous decay occurs
because excited electrons are unstable. They cannot exist in an excited
state for long, their average lifetime being about 10 to the power of negative eight
seconds long. Now when this spontaneous decay
occurs, the excited electron transitions down to a lower energy level, releasing a
photon in the process, which happens to have the same energy as the initial photon
that was absorbed and therefore the same energy as the difference in energy between
the electron energy levels. This is spontaneous emission.
But it’s not what we’re looking
for. We want to see stimulated emission,
which starts the same way as spontaneous, which is just having an electron in the
excited state. The difference between stimulated
and spontaneous emission is that in stimulated emission there is no spontaneous
decay that occurs. What happens instead is that
another photon comes in and interacts with the electron while it is already in its
excited state. But rather than being absorbed, the
photon stimulates the electron causing the electron to transition down in energy
level and release a photon, which has the same energy, direction, and phase as the
photon that caused the stimulation.
In order for this stimulated
emission to have occurred at all, it must’ve happened faster than 10 to the power of
negative eight seconds because otherwise there would’ve been a spontaneous decay
causing a spontaneous emission. Even though both the missions start
with the same condition of needing an excited electron, a stimulated emission
requires the electron to be stimulated by a photon, whereas in a spontaneous
emission we just have to wait for the excited electron to spontaneously decay. This means in stimulated emission
we should expect to see two photons on a diagram: one that caused the stimulation
and another one that’s emitted from the electron when it transitions downwards. But in spontaneous emission, we
should expect to only see one photon, since the spontaneous decay doesn’t need
another photon to stimulate it.
Looking at our answers, we know
that (A) cannot be correct, since a stimulated emission requires an electron to drop
down to an unexcited state. This stimulated emission is not
shown correctly because we should expect to see two entire photons after the
stimulated emission process, but we only see one. Therefore, the following way in
which the stimulated emission is incorrectly shown in this diagram is (B). Two photons should be shown.
