25.1.3 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:

• λ_max is the maximum wavelength emitted by the star at the peak intensity
• 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 full equation for Wien's Law is given by

λ_maxT = 2.9 × 10⁻³ m K

• Where:
  • λ_max = peak wavelength of the star (m)
  • T = thermodynamic temperature at the surface of the star (K)

• This equation tells us the higher the temperature of a body:
  • The shorter the wavelength at the peak intensity, so hotter stars tend to be white or blue and cooler stars tend to be red or yellow
  • The greater the intensity of the radiation at each wavelength

Table to compare surface temperature and star colour

Step 1: Write down Wien’s displacement law

λ_maxT = 2.9 × 10^-3 m K

Step 2: Rearrange for temperature T

Step 3: Calculate the surface temperature of each star

Step 4: Write a concluding sentence

Betelgeuse has a surface temperature of 3500 K, therefore, it is much cooler than Rigel

The Orion Constellation; cooler stars, such as Betelguese, appear red or yellow, while hotter stars, such as Rigel, appear white or blue