### Video Transcript

When the temperature of an object increases, what change occurs to the wavelength at which the object emits radiation with the greatest intensity?

The basic fact behind this exercise is that all objects, so long as they have a temperature above absolute zero, emit radiation. This radiation can be approximated using an idealized concept called the black body.

A black body is an object that absorbs all radiation incident on it, and it reemits the radiation according to a certain spectral profile. If we were to plot a black body’s radiated intensity versus its wavelength, that curve might look like this, where at some particular wavelength value, the radiation is at its most intense.

A particular black body radiation curve like this corresponds to a specific temperature. If we call the temperature of the black body that emits radiation like this 𝑇 sub one, we can imagine decreasing that temperature and replotting the black body curve. For a lesser temperature, 𝑇 sub two, the black body curve might look like this. For an even smaller temperature, perhaps like this, and so forth and so on, as the temperature of the black body decreases, so does the height of the radiation curve.

We can notice something else about this progression of black body curves. If we highlight the wavelength at which each respective curve has its radiation intensity maximum, we see that as the black body temperature goes down, that wavelength moves to the right; it increases.

A scientist named Wien made this observation and developed what’s called Wien’s displacement law about it. Wien noticed that if you take the wavelength at which a given blackbody radiates its greatest intensity and multiply that by the temperature of the black body, the product of those two values is a constant. That is, regardless of which temperature our black body is, when we multiply that temperature by the wavelength at which the radiation peaks, we’ll get the same value.

It’s Wien’s displacement law that lets us answer this question. We see that as the temperature of our object goes up, the wavelength at which the radiation has the greatest intensity moves to the left; that is, it decreases. And that’s the answer to how the wavelength changes when the temperature of the radiating object goes up.