Question Video: Determining Which Way a Stimulated Emission is Incorrectly Shown Physics

The diagram 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.

03:51

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.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.