Stellar Temperature from a Spectrum
A star emits a broad range of wavelengths. The position of the spectrum peak gives a surface-temperature estimate.
A hotter surface moves the peak to shorter wavelength
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A star is treated approximately as a black body. Wien's displacement law links the peak wavelength of its spectrum to its thermodynamic surface temperature.
Symbols
- = wavelength at maximum spectral intensity (m)
- = surface thermodynamic temperature (K)
- = Wien displacement constant, 2.90 × 10⁻³ (m K)
- Shorter peak wavelength means higher surface temperature.
- Longer peak wavelength means lower surface temperature.
- Convert nanometres to metres before using the constant in m K.
Worked example
Temperature from a 480 nm peak
Answer
Your turn9702/42/O/N/23 Q10(a) adapted
State Wien's displacement law and identify the two measured quantities. [2]
Show worked answer
The wavelength of maximum emission is inversely proportional to the thermodynamic surface temperature of the star. The two quantities are the peak wavelength and the surface thermodynamic temperature.
Common mistake
If redshift is not corrected, the observed peak wavelength is too large and Wien's law gives a surface temperature that is too low.