The diagram shows two curves, each of which represents the predicted electromagnetic radiation emission spectrum of a blackbody according to a different model of blackbody radiation. Which of the curves better corresponds to a model of blackbody radiation in which the number of electromagnetic waves emitted by a blackbody increases as the wavelength of the waves decreases and the number of such waves is not affected by other factors?
Taking a look at our diagram, we see these two curves: one in purple and one in blue. These two curves, we’re told, each represent a predicted electromagnetic radiation emission spectrum of a blackbody according to different models of blackbody radiation. So, according to one such model, we would get the purple curve. And according to another such model, we would get the blue one.
Our question asks us to identify which curve shows the number of electromagnetic waves emitted increasing as the wavelength of the waves involved decreases. So let’s think for a moment about decreasing wavelength. Our horizontal axis shows us the wavelengths over which these two curves are plotted. Decreasing in wavelength means moving in this direction along our graph. As we do that, if we follow the purple curve, we see that decreasing wavelength indicates increasing intensity. Then, if we follow the blue curve, the same thing seems to happen, up to a point.
On the blue curve, once our decreasing wavelength goes past this value marked 𝜆, we see the intensity of the radiation predicted by this model decreasing. We see, in fact, that the curve decreases so much that eventually it reaches zero. Therefore, no matter how high energy each emitted wave is, the blue curve corresponds to a model where, at short enough wavelength, zero waves are emitted.
On the other hand, according to the purple curve, the number of electromagnetic waves emitted seems to increase without limit as wavelength decreases. Of these two curves, we see that only the purple curve increases in intensity as wavelength decreases. And this corresponds to the number of electromagnetic waves emitted by a blackbody in this model. That answers part one of our question. Now let’s move on to part two.
For wavelengths greater than the peak wavelength of the spectrum shown by the blue curve, how does the difference between the intensities at given wavelengths predicted by the two models change as the wavelength increases? (A) The difference in intensity increases. (B) The difference in intensity decreases.
Okay, so we’re talking about wavelengths greater than the peak wavelength of the spectrum shown by the blue curve. That peak wavelength is here. And we’re considering wavelengths that are longer than this. As we move to longer wavelengths, we compare the intensities given by these two models. And we see how those intensities change as wavelength increases.
We can see that, starting at the peak wavelength of its spectrum, following the blue curve, we get this line. Tracing the purple curve gives us this line. And we want to know how at representative wavelengths, say this wavelength here and this wavelength right here, the difference in intensities marked out by these two curves changes.
Let’s look first at the difference in intensities of these two curves along this wavelength we’ll call 𝜆 one. That difference is shown by the length of this green line. If we move farther on then to this next wavelength we’ll call 𝜆 two, we can see the difference in intensity between the two curves is much smaller. So, as we moved from a shorter wavelength to a longer one, the difference in intensity between our two curves decreased. That difference, after all, is indicated by the length of these vertical green lines. This discovery corresponds to answer option (B). As wavelength increases beyond the wavelength of the peak of the blue curve, the difference in intensity between the blue and the purple curve decreases.