Video: Calculating the Temperature of an Object from its Peak Radiation Emission Wavelength

The radiant energy from the Sun reaches its maximum at a wavelength of about 0.5 𝜇m. What is the approximate temperature of the Sun’s surface?

02:12

Video Transcript

The radiant energy from the Sun reaches its maximum at a wavelength of about 0.5 micrometers. What is the approximate temperature of the Sun’s surface?

In this example, we’ll treat the Sun as a black body. A black body is an object that perfectly absorbs all radiation incident on it. The black body get its name from the fact that if we looked at it, it would look black. That’s because it absorbs all the radiation reaching it.

Even though black bodies don’t reflect any light, they do emit light. If we were to plot the emission of light from a black body, its power vs its wavelength, the curve might look something like this, where the power that’s emitted by the black body depends on the wavelength. The characteristic parameter of a blackbody is its temperature, capital 𝑇. And if we plotted at the curves of several different black bodies, that is black bodies at different temperatures, then an interesting phenomenon begins to emerge.

Notice that each of these curves has a peak value, some wavelength value at which the black body radiates more light than at any other. A scientist by the name of Wien made an interesting discovery about this wavelength. Wien discovered that if you look at the wavelength at which a given blackbody radiates its most energy and you multiply that wavelength by the temperature of the black body, that product is a constant value.

So for any temperature blackbody, if you multiply that temperature by the wavelength at which the black body radiates its most light, you’ll get the same number. And that number Wien found is approximately 2.898 times 10 to the negative third meters Kelvin.

In our case, we want to solve for the temperature of the Sun’s surface. And we could solve for that temperature, assuming the Sun is a black body, by dividing this constant value by the given wavelength for the peak of the Sun’s radiation. To make the units consistent, we’ll convert our wavelength into units of meters to agree with the constant value. To one significant figure, our result is 6000 Kelvin. That’s the approximate surface temperature of the Sun based on the wavelength of its maximum radiation.

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