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Black Body Radiation

Physics: AQA A Level, topic 9.2.3

Black Body Radiation

Stars can be modelled very accurately as black bodies.

Black body

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.
Temperature and wavelength

Temperature and wavelength

  • The diagram also shows that stars of different temperatures have different distributions, characterised by the wavelength of maximum intensity.
Colour

Colour

  • 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.

Stefan's law

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.
Find size of star

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).

Wien's displacement law

Wien's displacement law

  • The wavelength at which the star emits light most intensely:
  • λmax×T=constant=2.9×10−3\lambda_{max}\times T= constant = 2.9\times 10^{-3}mK
Application

Application

  • 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.

Test yourself on Black Body Radiation

  • What colour are cool stars?

  • Which of these statements are true about star colours?

  • Stefan's law is P=σAT4P=\sigma A T^4. What unit is surface area measured in?

  • Stefan's law is P=σAT4P=\sigma A T^4. What unit is temperature measured in?

  • Which of these units are used in Stefan's law?

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