Video Transcript
Pick the word that would correctly complete the following statement about the emission of electromagnetic radiation by an ideal blackbody. The electromagnetic-radiation- emission spectrum of an ideal blackbody is blank the spectrum of the radiation that the blackbody absorbs. (A) The inverse of, (B) the same as, (C) independent of.
Okay, so we want to figure out which of these answer choices correctly goes in this blank here in our statement. The statement compares an ideal blackbody’s emission spectrum with that blackbody’s absorption spectrum. Emission and absorption are opposite processes. When we talk about absorption or thinking of a blackbody that has electromagnetic radiation incident on it, this radiation could have any wavelength or any intensity. Regardless, an ideal blackbody will absorb it. That’s actually how blackbodies get their name from the fact that they absorb all light incident on them, so they appear black. This means that if we were to make a graph that plotted the absorption of a blackbody against the wavelength of the incoming radiation, that graph in a sense wouldn’t be very interesting.
If perfect absorption corresponded to an absorption of one, then we would have a horizontal line at this absorption level for all wavelengths. This is the absorption spectrum of an ideal blackbody. But then, what about emission? Emission, of course, is the process of the object, in this case a blackbody, emitting radiation. An ideal blackbody does emit radiation. It doesn’t just absorb everything and then heat up hotter and hotter and hotter. But unlike for the absorption spectrum, it doesn’t treat all wavelengths the same in emission. For a blackbody at a given temperature, its emission-versus-wavelength curve would look something like this. Note that even at the wavelength of peak emission, it’s not emitting 100 percent of light of that wavelength that’s incident on the blackbody.
By comparing these absorption and emission curves, we can make some progress with our answer. Answer option (A) says that the emission curve of an ideal blackbody, that’s this curve over here, is the inverse of the absorption curve here. We see, though, that that’s not the case. If that were true, then the emission curve would look like this, an emission of zero at all wavelengths. We won’t choose option (A) as our answer. Option (B) claims that the emission curve of an ideal blackbody is the same as that blackbody’s absorption curve. Once again, though, by comparing our absorption and emission curves, we see that this is not the case. While an ideal blackbody does emit some radiation, it doesn’t emit it the same way that the blackbody absorbs it. That is, it doesn’t emit equally and perfectly at all wavelengths.
The answer choice we’re left with is option (C), which says that the emission curve is independent of the absorption curve. This is the answer option that makes the most sense. There isn’t any clear mathematical relationship between this graph and this graph. It’s reasonable to think that the two are independent of one another. And indeed, from what more we know about blackbodies, we know that the shape of this curve depends on the blackbody temperature. Temperature, however, has no impact on the absorption curve of a blackbody. It’s true then that these curves are independent of one another. Our completed statement reads like this: The electromagnetic-radiation-emission spectrum of an ideal blackbody is independent of the spectrum of the radiation that the blackbody absorbs.
