Video Transcript
The diagram shows the transition of an electron in a hydrogen atom from 𝑛 equals two to 𝑛 equals one, emitting a photon as it does so. What is the energy of the photon in electron volts? Give your answer to one decimal place. What is the energy of the photon in joules? Give your answer in scientific notation to two decimal places.
The answers to both parts of this question will have the same value. They’ll just be represented by different units of energy. Let’s begin with the first part and calculate the photon’s energy in electron volts. Now, because the electron is transitioning down a level, energy must be transferred away from it. And this energy is transferred via the photon. Recall that the energy difference between the electron’s initial and final levels, which we call 𝛥𝐸, corresponds to or has the same value as the energy of the emitted photon.
We can calculate 𝛥𝐸 and therefore the energy of the photon by subtracting the binding energy at level one from the binding energy at level two. These values are given in the diagram, so let’s substitute them in. And we have 𝛥𝐸 equals negative 3.40 electron volts minus negative 13.6 electron volts, which to one decimal place equals 10.2 electron volts. This is the energy transferred away from the electron by means of the photon. Therefore, the energy of the photon is 10.2 electron volts.
Now, moving on to the second part of the question, we basically just need to convert the photon’s energy from electron volts to joules. To do this, recall that one electron volt equals 1.60 times 10 to the negative 19 joules. So we can multiply the photon’s energy that we found earlier by this conversion factor, which itself is just equal to one, and cancel out units of electron volts. Then, plugging this into a calculator, we get 1.6320 times 10 to the negative 18 joules. This value is already in scientific notation, so we just need to round it to two decimal places. And thus, the energy of the photon is 1.63 times 10 to the negative 18 joules.
At this point, we might notice how much easier it is to work with a number like 10.2 than 1.63 times 10 to the negative 18. This is a good illustration of how it can be more convenient to use electron volts over joules in certain contexts although they both measure energy and these two values we calculated are equivalent. And so we have seen how to express the energy of the emitted photon using both electron volts and joules.
