Video Transcript
A scientist has a gas canister that contains a mixture of unknown gases. In order to identify which gases are in the mixture, she looks at the spectrum of visible light emitted from it when it is heated. This is shown in the figure. Also shown in the figure are the emission spectra of several pure, gaseous elements. Which of the five elements does the mixture contain?
In the figure mentioned in the statement, we have the observed spectrum as well as the emission spectra of hydrogen, helium, oxygen, nitrogen, and argon. We know that these are emission spectra because they have many bright lines separated by dark areas. If they were absorption spectra, the lines would be in exactly the same places, but the lines would be dark and the spaces in between would be colored. The lines will be in the same place because spectral lines are due to electrons transitioning between energy levels within an atom or molecule. These transitions always occur with the same energy whether they are absorbing or emitting.
Additionally, because every kind of atom and molecule has its own unique energy level structure, absorption and emission spectra are unique to that particular type of atom or molecule. When we have a mixture of atoms or molecules, the overall spectrum will be the combination of the spectra of each of the individual components because each component will emit or absorb its own spectrum. Importantly, this is only true of a mixture. But, for example, if we mix hydrogen and oxygen and then they react to form water, well water is a new compound and so it has its own unique spectrum that is not a simple combination of hydrogen and oxygen.
Now, because spectra are unique and they combine in a mixture, we can determine if a particular element or molecule is present in a mixture by matching up a reference spectrum of the pure substance to the observed spectrum. Indeed, that’s what we’ll do in this problem. We will match up each of our five reference spectra to the spectrum we observe. And if all of the lines from the reference spectrum appear in the observed spectrum and the reference spectrum doesn’t have any extra lines that don’t appear in the observed spectrum, we will know that that element is in our mixture.
Now, because there are so many lines in the observed spectrum, it will be somewhat difficult to determine which lines are actually present just by looking. One way to deal with this would be to take a ruler and extend each of the spectral lines from the reference spectra up to the observed spectrum. For example, from the line we just drew, we can conclude that hydrogen is not one of the elements in our mixture because the spectral line at 655 nanometers does not appear in the observed spectrum. However, if we did this for each spectral line, we would wind up with a lot of clutter. And some of these spectra have some very closely spaced clusters of lines, which also makes this process difficult. So what we will instead do is present each spectrum one at a time directly beneath the observed spectrum so we can immediately and visually see if they match up.
Here is the hydrogen spectrum we just looked at. As we saw, the red line doesn’t match, and as we can now see, the teal line doesn’t match either. Based on this alone, we can safely conclude that hydrogen is not one of the elements in our mixture. And it turns out if we look very closely, this blue line and this violet line also don’t appear in the observed spectrum. However, when we turn to helium, we can see that all of the lines in the helium spectrum do appear in the observed spectrum. Particularly, this distinctive green doublet and also these two violet doublets appear in both spectra, but all the other lines also do as well.
Importantly also, there are no lines that appear in the helium spectrum that do not appear in the observed spectrum. There are however many lines in the observed spectrum that don’t appear in the helium spectrum. Those just come from other elements. So because the entire helium spectrum is contained in our observed spectrum, we can safely conclude that helium is one of the elements in our mixture. The same is true for oxygen. There are lines in our observed spectrum that match up to each of the lines in the oxygen spectrum. So because the oxygen spectrum is completely contained in the observed spectrum, we can safely conclude that oxygen is one of the gases in our mixture. This is also true of nitrogen.
As we can see from this image, the nitrogen spectrum is completely contained in our observed spectrum. Particularly notable are these two large clusters of lines in the red portion of the spectrum. Whenever we see features like this in an observed spectrum, it is likely that our sample contains nitrogen. Finally, we consider argon. A reference spectrum for argon has quite a few lines in it, but each and every one of those lines also appears in the observed spectrum. So once again, we find that the spectrum for argon is completely contained in our observed spectrum. So argon must be one of the gases in our mixture.
Since we did find the complete spectra for helium, oxygen, nitrogen, and argon in our observed spectrum but did not find the complete spectrum for hydrogen, we conclude that of our five choices, helium, oxygen, nitrogen, and argon are the four that appear in our mixture.
