How Do You Find a Star's Temperature From Its Emission Spectrum?

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Rearranging gives:

The wavelength must be converted to metres, and the resulting temperature is measured in kelvin.

Physically, a hotter stellar surface emits more strongly at shorter wavelengths, so the entire black-body curve shifts toward a smaller $\lambda_{\max}$. Wien's law therefore gives an inverse relationship: doubling the absolute temperature halves the peak wavelength.

For example, suppose a star's emission spectrum has its maximum intensity at $500\ \text{nm}$:

Therefore,

The star's surface temperature is approximately $5800\ \text{K}$.

If the peak is read from a graph, use the top of the smooth continuous curve rather than a narrow spectral line. State a sensible reading uncertainty if the scale limits precision. Because real stars only approximate ideal black bodies, the result estimates the photosphere's effective surface temperature.

A common misconception is that the individual bright or dark spectral lines directly give the star's temperature. For this IB B.1 calculation, temperature is found from the peak of the overall black-body curve, while spectral lines mainly identify elements.

Exam Technique

In a Calculate question, show the peak wavelength, convert it to metres, rearrange Wien's law, substitute, and give the answer in kelvin. Do not estimate temperature from the star's visible colour alone when a spectrum or graph is provided.