Video Transcript
A scientist has a sample of an unknown gas. In order to identify it, she shines a continuous spectrum of white light through the gas and observes which wavelengths of light are absorbed by it. This is shown in the figure, as well as the absorption spectra of five pure gaseous elements. Which of the five elements is the unknown gas?
Having a look at the figure that we’re given, we can see that it shows a series of absorption spectra. Up at the top, we’ve got the spectrum of the unknown gas that the scientist wants to identify. Then shown below this, we’ve got the absorption spectra of helium, oxygen, neon, argon, and xenon. We’re being asked to identify which of these five elements is the unknown gas. Now, since we’re asked which element the unknown gas is, this means we know we can assume that this gas is a pure sample. That is, it’s not a mixture of some number of different elements, but rather it’s entirely one of these five elements whose absorption spectra we’re shown here.
What we need to do, then, is to identify a match between this absorption spectrum of the unknown gas and one of these five spectra shown below. If we look at the absorption spectrum of the unknown gas, we can see that we’ve got a continuous spectrum, but with a whole load of these black lines in it. Let’s recall that we’re told that a continuous spectrum of white light is shone through the gas. And so that’s why we see this continuous spectrum. Each of these black lines in the spectrum indicates a wavelength that is missing from the light after it has passed through the sample of gas. That is, these black lines tell us the wavelengths of light that are absorbed by this particular gas.
We can notice that at the top of this figure, we’ve got a wavelength scale that allows us to read off the numerical values of these absorbed wavelengths. So, for example, we can see that this line here in the absorption spectrum of the unknown gas has a wavelength of about 583 nanometers. Meanwhile, we can see that the wavelength of this absorption line is around 682 nanometers. Now we can see that there’s a whole load of these lines in the absorption spectrum of the unknown gas. So we’re not going to individually read off the wavelength of each one because that would take us a really long time.
The important thing to realize is that an absorption spectrum acts kind of like a fingerprint for a particular element. This means that if we take this helium spectrum, for example, then any helium gas that we find anywhere in the universe will produce this exact same absorption spectrum with the exact same lines at the exact same wavelengths. So if we see an absorption spectrum that looks exactly like this one, then we know that we’re looking at an absorption spectrum of helium. Of course, the same holds true for the absorption spectrum of any other element, and that includes these four that were also given in this question.
What this means for us in this question is that in order for one of these elements to be a match for the sample of the unknown gas, that element’s absorption spectrum must contain all of the absorption lines that are present in the absorption spectrum of the unknown gas. And it must also contain no absorption lines that are not present in this unknown gas spectrum.
Now, we can make these comparisons by eye, and let’s begin with the absorption spectrum of helium. We can see that in the helium spectrum there’s a whole load of absorption lines at shorter wavelengths that are not present in the spectrum of the unknown gas. We can also notice that there are several absorption lines, such as these ones, that are present in the spectrum of the unknown gas but are not present in the spectrum of helium. Clearly, then, the helium spectrum does not match the spectrum from the unknown gas. And so this gas cannot be a sample of helium.
Next, let’s have a look at the absorption spectrum of oxygen. We can see that there’s two lines here in the oxygen spectrum that are not present in the spectrum of the unknown gas. So then, without even looking any further along these two spectra, we can already say that they don’t match. And so the unknown gas cannot be oxygen.
Let’s now move on to the absorption spectrum of neon. We can see that the shortest wavelength line in the neon spectrum is this one right here. If we trace vertically upward to the wavelength scale from this absorption line in neon, we see that it’s at a wavelength of about 454 nanometers. Importantly, if we look at the same wavelength in the spectrum of the unknown gas, we see that there’s no absorption line present. Instead, the shortest wavelength line in this unknown gas absorption spectrum is this line here, which appears to occur at a wavelength of about 475 nanometers. Since we’ve identified a line that is present in the neon absorption spectrum but is not present in the absorption spectrum of the unknown gas, then we know that the unknown gas is not neon.
Now, let’s take a look at the absorption spectrum of argon. We can notice that this spectrum has all these absorption lines at short values of wavelength that are not present in the absorption spectrum of the unknown gas. This means that the two spectra don’t match, and so the unknown gas cannot be argon.
This just leaves us with the absorption spectrum of xenon. This spectrum looks a lot more promising. For a start, at these short values of wavelength below about 470 nanometers or so where we have no absorption lines in the spectrum from the unknown gas, we can see that there are also no absorption lines in this wavelength range in the spectrum of xenon. Similarly, at longer wavelengths from about 610 nanometers upwards where we’ve got loads of absorption lines in the spectrum from the unknown gas, there are also a whole load of lines in the spectrum of xenon.
There’s also some other tricks we can use to help convince ourselves that these two spectra really do match. One technique is to pick some specific absorption lines in the xenon spectrum and draw vertical lines upward until we get to the spectrum of the unknown gas. We can then see that these absorption lines in the xenon spectrum have corresponding lines at the exact same wavelength in the spectrum from the unknown gas.
Then another technique we can use is to look for individual easily identifiable features in the absorption spectrum from xenon and see if those features also occur in the spectrum from the unknown gas. For example, in the unknown gas spectrum, we can see that at about 493 nanometers we’ve got these two absorption lines really close together. If we then look at the same wavelength value in the spectrum of xenon, we can see that we’ve also got these two really closely spaced lines.
Now from here, we could in principle go on to compare these two spectrum more closely, checking that every single absorption line in the unknown gas spectrum occurs at exactly the same wavelength as every single line in the spectrum of xenon. However, we’ve already eliminated the other four spectra and shown that none of them can be a match for the unknown gas. We’ve also explicitly traced up individual lines from the xenon spectrum to see that they occur at the same wavelengths in the spectrum from the unknown gas.
We have also noted other things that are common to both of these spectra, such as the absence of any absorption lines at shorter wavelengths and the presence of a lot of absorption lines at longer wavelengths. Further still, we’ve identified this double-line feature in the absorption spectrum from the unknown gas and the spectrum from xenon. All in all then, we can be fairly confident that this absorption spectrum of xenon is a match for the spectrum of the unknown gas. This match between the absorption spectra tells us that the unknown gas is xenon.