OCR · A-Level · Physics
Course version: H556 · Version from Sept 2015
(k) use of Wien’s displacement law and Stefan’s law to estimate the radius…
Full specification wording
Electromagnetic radiation from stars: (k) use of Wien’s displacement law and Stefan’s law to estimate the radius of a star.
Wien’s displacement law, λmaxT = 2.9 × 10⁻³ m K, links a star’s peak-emission wavelength λmax to its surface temperature T. Stefan’s law, L = 4πr²σT⁴, links luminosity, radius and temperature.
Checked against the OCR H556 specification (opens in a new tab) on .
- Point 11 of 11
- 4 key terms
Study notes
From the checked teaching notes for this specification point.
The idea
Wien’s displacement law, λmaxT = 2.9 × 10⁻³ m K, links a star’s peak-emission wavelength λmax to its surface temperature T. Stefan’s law, L = 4πr²σT⁴, links luminosity, radius and temperature. To estimate a star’s radius: measure λmax from its spectrum, use Wien’s law to find T = (2.9 × 10⁻³) / λmax, then rearrange Stefan’s law to r = √(L / (4πσT⁴)). Luminosity may be given or inferred from apparent brightness and distance. Work in kelvin and metres throughout. This two-step method is powerful because it needs only the spectrum and the luminosity.
What earns the marks
- Wien’s displacement law is λmaxT = 2.9 × 10⁻³ m K, where λmax is the wavelength of peak emission.
- Use Wien’s law to calculate surface temperature from the observed peak wavelength: T = (2.9 × 10⁻³) / λmax.
- Stefan’s law L = 4πr²σT⁴ relates luminosity, radius and temperature.
- Rearrange Stefan’s law to r = √(L / (4πσT⁴)) and substitute the temperature found from Wien’s law.
- Luminosity may be supplied directly or deduced from apparent brightness and distance before the radius calculation.
- Keep all quantities in SI units: λmax in metres, T in kelvin, L in watts and r in metres.
Common mistakes and how to put them right
Using Wien’s law to find radius directly.
Put it right: Wien’s law gives temperature only, and radius requires Stefan’s law as a second step.
Substituting λmax in nanometres without converting to metres.
Put it right: Convert nm to m by multiplying by 10⁻⁹ before dividing into the constant.
Mixing up the order of operations and squaring the temperature before dividing.
Put it right: Compute T⁴, multiply by 4πσ, then divide L by that product before taking the square root.
Assuming the star is a perfect black body without comment.
Put it right: State that the estimate assumes black-body behaviour, which is an approximation.
Exam tips
- Show both equations explicitly and label the intermediate temperature before calculating the radius.
- Carry extra significant figures through the intermediate temperature to avoid rounding errors in the final radius.
- State the black-body assumption when interpreting the estimate, since real stellar spectra deviate from a perfect black body.
Try the lesson
The start of the Electromagnetic radiation from stars: (k) use of Wien’s displacement law and Stefan’s law to estimate the radius of a star. lesson, made from checked teaching notes for this specification point.
Listen
Wien’s displacement law, λmaxT = 2.9 × 10⁻³ m K, links a star’s peak-emission wavelength λmax to its surface temperature T. Stefan’s law, L = 4πr²σT⁴, links luminosity, radius and temperature. To estimate a star’s radius: measure λmax from its spectrum, use Wien’s law to find T = (2.9 × 10⁻³) / λmax, then rearrange Stefan’s law to r = √(L / (4πσT⁴)). Luminosity may be given or inferred from apparent brightness and distance. Work in kelvin and metres throughout. This two-step method is powerful because it needs only the spectrum and the luminosity. A strong answer earns marks for these points. Wien’s displacement law is λmaxT = 2.9 × 10⁻³ m K, where λmax is the wavelength of peak emission. Use Wien’s law to calculate surface temperature from the observed peak wavelength: T = (2.9 × 10⁻³) / λmax. Stefan’s law L = 4πr²σT⁴ relates luminosity, radius and temperature. Rearrange Stefan’s law to r = √(L / (4πσT⁴)) and substitute the temperature found from Wien’s law. A common slip: Using Wien’s law to find radius directly. Instead, Wien’s law gives temperature only, and radius requires Stefan’s law as a second step. Exam tip: Show both equations explicitly and label the intermediate temperature before calculating the radius.
See it
Key words
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Wien’s displacement law
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Stefan’s law
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Luminosity
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Black-body modelling of stars
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See every definition
- Wien’s displacement law
- λmaxT = 2.9 × 10⁻³ m K, where λmax is the wavelength of peak emission, linking a star’s peak-emission wavelength to its surface temperature.
- Stefan’s law
- L = 4πr²σT⁴, which relates luminosity, radius and temperature.
- Luminosity
- A quantity that may be given or inferred from apparent brightness and distance, and is used in Stefan’s law.
- Black-body modelling of stars
- An estimate that assumes black-body behaviour, which is an approximation since real stellar spectra deviate from a perfect black body.
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