Black Body Radiation

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Black Body Radiation

Stars can be modelled very accurately as black bodies.

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Black body

  • A black body is defined as the universal emitter.
  • At a given temperature, the intensity of light at each wavelength follows the curve shown in the diagram.
  • Stars are assumed to be black bodies.
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Temperature and wavelength

  • The diagram also shows that stars of different temperatures have different distributions, characterised by the wavelength of maximum intensity.
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  • A star’s colour is related to this distribution:
    • Cool stars are more red in colour.
    • Warmer stars are white as they emit roughly equally across the visible spectrum.
    • Very hot stars appear blue.

Stefan's Law

Stefan’s Law and Wien’s Displacement Law are two ideas that assist in measuring and comparing the power outputs, temperatures and sizes of stars.

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Stefan's law

  • Power output of star:
    • P=σ×A×T4P=\sigma \times A \times T^4
  • Where T is the temperature (in Kelvin) of the surface of the star, A is the surface area of the star and σ (sigma) is Stefan’s constant.
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Find size of star

  • If we know the temperature and power emitted by a star, we can work out its surface area, A, and therefore its radius (assuming the star is a perfect sphere).

Wien's Displacement Law

Wien’s Displacement law describes the relationship between the wavelength of maximum intensity, λ, and T, the surface temperature of the star (in Kelvin).

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Wien's displacement law

  • The wavelength at which the star emits light most intensely:
  • λmax×T=constant=2.9×103\lambda_{max}\times T= constant = 2.9\times 10^{-3}mK
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  • Astronomers can measure the intensity of light from a star at the Earth and the distance of the star from the Earth.
  • Wien’s displacement law allows an estimate of the temperature of the star to be made.
  • Stefan’s Law can then be used to estimate the radius of the star.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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