9.2.3

# Black Body Radiation

Test yourself

## Black Body Radiation

Stars can be modelled very accurately as black bodies.

### 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

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

### 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

• Power output of star:
• $P=\sigma \times A \times T^4$
• 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

• 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

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

### 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.