Wien's Displacement Law (Cambridge (CIE) A Level Physics): Revision Note

Wien's displacement law

• Wien’s displacement law relates the observed wavelength of light from a star to its surface temperature, it states:

  The black body radiation curve for different temperatures peaks at a wavelength which is inversely proportional to the temperature

• This relation can be written as:

${\lambda }_{max}\propto \frac{1}{T}$

• Where

  • ${\lambda }_{max}$ = the maximum wavelength emitted by the star at the peak intensity (m)

  • $T$ = thermodynamic temperature at the surface of the star (K)

• A black body is an object which:

  • absorbs all the radiation that falls on it, and is also a good emitter

  • does not reflect or transmit any radiation

• A black-body is a theoretical object, however, stars are the best approximation there is

• The radiation emitted from a black-body has a characteristic spectrum that is determined by the temperature alone

The intensity-wavelength graph shows how thermodynamic temperature links to the peak wavelength for four different stars

• The constant of proportionality in Wien's law is given by

${\lambda }_{max}T=2.9\times {10}^{-3}\mathrm{m}\mathrm{K}$

• This equation tells us the higher the temperature of a body:

  • the shorter the wavelength at the peak intensity

  • the greater the intensity of the radiation at each wavelength

• This means that hotter stars tend to be white or blue and cooler stars tend to be red or yellow

Table to compare surface temperature and star colour