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What is described by Planck’s law?

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Video Transcript

What is described by Planck’s law?

Now Planck’s law is the relationship between a black body’s radiation intensity distribution and wavelength. Okay, now that’s a lot of complicated words in one sentence. So let’s break all of that down. First of all, what’s a black body? Well, let’s assume that this is a black body. This is an object that perfectly absorbs all of the radiation that’s falling on it. In other words, if we have a beam of light falling onto this black body, then all of it gets absorbed by the black body and none of it is reflected.

Now a black body, when it reaches thermal equilibrium or, in other words, is at the same temperature as its surroundings, will also emit some of the energy that it absorbs. And of course, because it’s in thermal equilibrium, because it’s at the same temperature as its surroundings, the amount of energy that it emits is the same as the amount of energy that it absorbs.

However, that does not necessarily pose a limit on the wavelengths or frequencies of radiation that the black body can emit. And a black body showcases a very particular emission spectrum. So if we draw a plot of the intensity of radiation emitted by a black body, which we place on the vertical axis, and the wavelength of the emitted radiation on the horizontal axis, then we will see that the spectrum showing the radiation from the black body is a very particular shape. And specifically, it has a peak value at one certain wavelength. Let’s call that wavelength 𝜆 subscript p for peak wavelength.

Now this peak wavelength will shift depending on the temperature of the black body. But not only this, the value of the maximum radiation intensity changes as well depending on the temperature. So, for example, this lower curve over here shows the black body radiation spectrum for a slightly lower temperature, which is why its peak wavelength is now here. In other words, the peak wavelength has increased, and the maximum intensity has decreased. Or conversely, the radiation spectrum for a black body at a much higher temperature than before has a peak wavelength that’s lower than before. And the maximum intensity is higher than before.

Now these temperature-dependent spectra that show the radiation intensity emitted by a black body are what is described by Planck’s law. And hence, we can say that Planck’s law describes the distribution of radiation intensity with wavelength emitted from a black body.

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