Video Transcript
An astronomer looks at the spectrum of light from a distant star. The spectrum he sees is shown in the figure. He compares the emission lines within the spectrum to the emission lines in the spectra of pure elements, which are also shown in the figure, in order to identify which elements are present in the outer layers of the star. State all of the elements that are present in the outer layers of the star.
The figure referenced in the statement is this one down here with the emission spectrum observed by the astronomer as well as five reference spectra for hydrogen, helium, boron, carbon, and oxygen.
Whenever we are interested in emission or absorption spectra, we always need to keep in mind that atomic and molecular spectra are unique. When we say unique, we mean that all hydrogen atoms have the same spectrum, and this spectrum is different from all helium atoms and all boron atoms et cetera. The reason this is true is because these spectra come from electrons transitioning between energy levels within the atom or molecule. And every atom and molecule has its own unique set of electron energy levels.
We can use this fact to identify atoms and molecules by comparing an unknown spectrum to reference spectra, like we are doing in this question. When we have a single atom or molecule in our sample, this is enough. But when we have a mixture of multiple atoms or molecules, we need to recall that spectra add. So if we had a mixture of hydrogen and oxygen, the spectrum for the mixture would be a combination of the spectrum for hydrogen and the spectrum for oxygen.
It’s important to understand though that this would not be the case if the hydrogen and oxygen reacted to form water. Water would have a different spectrum than either hydrogen or oxygen because being a molecule, it has its own unique set of electron energy levels.
Anyway, we now need to compare each of these reference spectra to the observed spectrum to see if the lines match or not. Looking at the oxygen reference spectrum, we see that there are several lines stretching from the yellow to the red portion of the spectrum. And these lines are completely absent in our observed spectrum. If oxygen were in the outer layers of the star, we would see these red and yellow lines in the observed spectrum. Since we don’t, we can safely conclude that oxygen is not in the outer layers of the star.
Looking at the carbon reference spectrum, the first thing that we notice is this very wide bright line in the yellow portion of the spectrum around 600 nanometers. This feature is very distinctive, and it does indeed appear in the observed spectrum. The reason to start with distinctive features is that it can often be very difficult to distinguish between two lines that are very close together or very faint. So when we have a large feature like this yellow line, it’s good to start by checking that feature because it will be very obvious if it is present or absent.
Since this yellow line appears in both the carbon spectrum and the observed spectrum, let’s check out the other lines in the carbon spectrum. All of the other lines in the carbon spectrum have exact matches in the observed spectrum, except for this green line. In the observed spectrum, there is a bright wide green line at that position. This may be simply a result of adding two lines that are very close together, but it could be another feature entirely. So we can’t yet conclude whether or not carbon is in the outer layers of the star.
Turning to boron though, we can immediately conclude that boron is not in the outer layers of the star, because this orange line and this purple line do not have counterparts in the observed spectrum. Although the other three lines look like they might appear in the observed spectrum — and indeed, it can be hard to determine whether or not they do — the two lines we’ve marked certainly do not appear in the observed spectrum. So we are certain that boron does not contribute to what we see.
The helium spectrum has a few notable features we can check immediately: two pairs of lines in the purple region and one cluster of three lines in the blue region. If we ignore this blue line and this purple line from the observed spectrum, we see that we exactly have those two pairs of purple lines and the cluster of three blue lines that we see in helium. So if those two lines come from another spectrum, which it’s entirely likely that they do, we have pretty good evidence that helium is in the observed spectrum.
Taking a look at the remaining lines, we see that the blue line, teal line, orange line, and two red lines both have exact counterparts in the observed spectrum. However, when we come to the pair of green lines, we run into exactly the same wide green line that gave us trouble when it came to carbon. Actually though, this solves our problem. The combination of the carbon line and the line to the right in the helium would give us a wide green line in the observed spectrum if their wavelengths were ever so slightly different. So combining the double line from helium and the single line from carbon would give us this feature in an observed spectrum.
Therefore, we have concluded that all of the carbon lines and all of the helium lines both match up with the observed spectrum. So the observed spectrum contains both carbon and helium.
The remaining lines in the observed spectrum that we have not yet accounted for are this purple line, this blue line, this teal line, and this red line, which are exactly the lines of the hydrogen spectrum. So hydrogen is also one of the elements that contributes to the observed spectrum. In fact, between hydrogen, helium, and carbon, we have accounted for all of the lines of the observed spectrum.
We therefore conclude that of the five elements we started with, hydrogen, helium, and carbon are the three that are present in the outer layer of the star.
