# Wien's Law and Black-body Radiation

The brightness (or luminosity) of a star depends upon its temperature, which in turn determines the star's colour. This can be inferred by using photometry to calculate a colour index. This is because stars produce the majority of their light as perfect thermal radiators (known as black-bodies). Figure 1: Black-body curves for three stellar temperatures (the x-axis represents the light's wavelength from violet to red - the y-axis represents the amount of light at a given wavelength). Credit: National Schools' Observatory
Here, light (electromagnetic radiation) is produced over a range of wavelengths, but with a 'peak' brightness at a specific colour or wavelength called λmaxAs can be seen in the diagram above, stars of 12,000 K and hotter tend to have peak emission at UV wavelengths, whereas stars at around 8000 K emit primarily in the blue part of the optical spectrum. λmax depends only on the temperature of the radiating body (usually called the Effective Temperature, Teff) and is given by Wien's Law:

λmax Teff = 2.898 × 10-3 m K

Note that the m and K (metres and kelvin) are included in the equation to make the units balance.

An example of the use of this equation is the Sun, whose peak wavelength is at around 500 nm (5 x 10-7 m)

So Teff (in kelvin) = 2.898 × 10-3 5 x 10-7 = 5800 K

The HyperPhysics website contains an online calculator to convert temperature to peak wavelength, frequency, photon energy.

So measuring the colour of a star allows us to produce a reliable estimate of its temperature. The simplest way of doing this is by use of colour filters