# Wein's Displacement Law(OCR A Level Physics)

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Katie M

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Physics

## Wien's Law

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

• Wien's Law equation is given by:

λmaxT = 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

#### 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.

Determine which of these two stars, Betelgeuse or Rigel, is cooler.

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

λmaxT = 2.9 × 103 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

#### Exam 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.

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