Example 5.3: Calculating the Temperature of a Blackbody

We can use Wien's law to calculate the temperature of a star provided we know the wavelength of peak intensity for its spectrum. If the emitted radiation from a red dwarf star has a wavelength of maximum power at 1200 nm, what is the temperature of this star, assuming it is a blackbody?

Solution

Solving Wien's law for temperature gives:

$\displaystyle T=\frac{3\times10^{6}\,\text{nm K}}{\lambda_{\max}} =\frac{3\times10^{6}\,\text{nm K}}{1200\,\text{nm}} =2500\,\text{K}$

Check Your Learning

What is the temperature of a star whose maximum Light is emitted at a much shorter wavelength of 290 nm?

Answer:

$\displaystyle T=\frac{3\times10^{6}\,\text{nm K}}{\lambda_{\max}} =\frac{3\times10^{6}\,\text{nm K}}{290\,\text{nm}} =10{,}300\,\text{K}$

Since this star has a peak wavelength that is at a shorter wavelength (in the ultraviolet part of the spectrum) than that of our Sun (in the visible part of the spectrum), it should come as no surprise that its surface temperature is much hotter than our Sun's.

Bibliography

This example is a derivative work of the Creative Commons source in [1].

[1] Andrew Fraknoi, David Morrison, and Sidney Wolff, “Example 5.3: Calculating the Temperature of a Blackbody,” in “5.2 The Electromagnetic Spectrum,” Astronomy 2e. Houston, Texas: OpenStax, 2022. Licensed CC BY 4.0 in the original 2022 release (https://creativecommons.org/licenses/by/4.0/). Changes: converted to LaTeX and separated from its parent section as a standalone PhysicsLibrary example. Access for free at https://openstax.org/books/astronomy-2e/pages/1-introduction. Section source: https://openstax.org/books/astronomy-2e/pages/5-2-the-electromagnetic-spectrum.

"example of electromagnetic spectrum: calculating_temperature_of_a_blackbody" is owned by bloftin.
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