Wien's 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:
- λmax is the maximum wavelength (m) emitted by an object at the peak intensity
- T is the surface temperature (K) of an object
- Wien's Law equation is given by:
λmaxT = 2.9 × 10−3 m K
- This equation tells us 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
Worked example
The spectrum of the star Rigel in the constellation of Orion peaks at a wavelength of 263 nm, while the spectrum of the star Betelgeuse peaks at a wavelength of 828 nm.Which of these two stars is cooler, Betelgeuse or Rigel?
Step 1: Write down Wien’s displacement law
λmaxT = 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
Examiner Tip
Note that the temperature used in Wien’s Law is in Kelvin (K). Remember to convert from oC if the temperature is given in degrees in the question before using the Wien’s Law equation.
