5.11.6 Wein's Displacement Law

Black Body Radiator

• An ideal black body radiator is one that absorbs and emits all wavelengths. 
  • 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 bodies

Wien's Displacement Law

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

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

• This relation can be written as:

• Where:
  • λ_max = the maximum wavelength emitted by an object at the peak intensity (m) 
  • T = the surface temperature of an object (K) 

• Wien's Law equation is given by:

λ_maxT = 2.9 × 10⁻³ m K

• This equation shows that the higher the temperature of a body:
  • The shorter the wavelength at the peak intensity, so hotter objects tend to be white or blue, and cooler objects 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: List the known quantities

• • Maximum emission wavelength of Rigel = 263 nm = 263 × 10⁻⁹ m
  • Maximum emission wavelength of Betelgeuse = 828 × 10⁻⁹ m

Step 2: Write down Wien’s displacement law

λ_maxT = 2.9 × 10⁻³ m K

Step 3: 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