Estimate a star’s surface temperature with Wien’s law
Use the inverse relationship between peak wavelength and surface temperature.
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. Topic 25 was checked against Cambridge’s 2028–2030 syllabus; a full reconciliation of every remaining syllabus-year change is still outstanding. Online study supports the theory but cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use powers of ten, inverse-square relationships, proportional reasoning and SI units; distinguish wavelength, frequency, speed, flux and luminosity.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
According to Wien’s law, what happens to λmax when T increases?
What you will learn
- Use Wien’s displacement law λmax ∝ 1/T
- Estimate a star’s peak surface temperature from its spectrum
- Compare the temperatures of stars from peak wavelengths
Hotter stars peak at shorter wavelengths
Wien’s displacement law states λmax ∝ 1/T, where λmax is the wavelength at which the star’s emission spectrum peaks and T is its surface temperature. With the displacement constant b supplied, use λmax T = b.
Rearrange to T = b/λmax. Use wavelength in metres and b in m K to obtain temperature in kelvin. The inverse relation means halving the peak wavelength doubles the estimated temperature.
Compare peaks before comparing temperatures
A spectrum shifted towards shorter peak wavelengths indicates a higher surface temperature. A longer peak wavelength indicates a lower temperature under Wien’s law.
This comparison concerns the surface temperature inferred from the spectrum. It does not by itself tell you the star’s luminosity or distance.
Pause and explain
Which rearrangement estimates temperature from peak wavelength?
Worked example
A star has λmax = 5.80 × 10⁻⁷ m. Use b = 2.90 × 10⁻³ m K to estimate its surface temperature.
Show the worked solution
- Use λmax T = b.
- T = b/λmax = 2.90 × 10⁻³/(5.80 × 10⁻⁷).
- T = 5.00 × 10³ K.
Answer 5.00 × 10³ K.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A star’s spectrum peaks at 5.0 × 10⁻⁷ m. Estimate T using b = 2.90 × 10⁻³ m K.
Give me a hint
Divide the displacement constant by the peak wavelength.
Compare my reasoning
- T = b/λmax.
- T = 2.90 × 10⁻³/(5.0 × 10⁻⁷).
- T = 5.8 × 10³ K.
5.8 × 10³ K.
Look for these in your work
- Uses the inverse relationship
- Substitutes wavelength in metres
- Reports kelvin
Star A peaks at 400 nm and star B at 800 nm. Compare their surface temperatures using Wien’s law.
Give me a hint
For the same constant, compare reciprocal wavelengths.
Compare my reasoning
- Convert or compare the wavelength ratio: λB/λA = 800/400 = 2.
- Temperature is inversely proportional to peak wavelength.
- TA/TB = λB/λA = 2.
Star A is about twice as hot at the surface as star B.
Look for these in your work
- Recognises the inverse proportionality
- Uses the correct reciprocal ratio
- Identifies the hotter star
A measured peak wavelength is 580 nm. Convert it to metres and estimate the temperature with b = 2.90 × 10⁻³ m K.
Give me a hint
Convert nanometres before dividing.
Compare my reasoning
- 580 nm = 580 × 10⁻⁹ m = 5.80 × 10⁻⁷ m.
- T = 2.90 × 10⁻³/(5.80 × 10⁻⁷).
- T = 5.00 × 10³ K.
5.00 × 10³ K.
Look for these in your work
- Converts nm to m
- Applies T = b/λmax
- Reports the result in K
Common mistakes
- Using T proportional to λmax rather than inversely proportional
- Substituting nanometres without converting to metres if b is in m K
- Reporting a temperature in Celsius when the law gives kelvin
What can you explain now?
According to Wien’s law, what happens to λmax when T increases?
Compare with the explanation
λmax decreases
Peak wavelength is inversely proportional to temperature.
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Make it stick
How does a star’s peak wavelength change if its surface temperature doubles?
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