Wien's displacement law and stellar temperature

Overview

Wien's displacement law in words and value of Wien's constant.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   State Wien's displacement law in words.

   Model answer

   Wien's displacement law states that the wavelength at which a black body emits most strongly is inversely proportional to its absolute temperature.

2. 2

   State Wien's displacement law as an equation, defining every symbol and its unit.

   Model answer

   The law is λₘₐₓ T = W, where λₘₐₓ is the peak wavelength in metres (m), T is the absolute temperature in kelvin (K) and W is Wien's constant in m K.

3. 3

   What is the value of Wien's constant?

   Model answer

   Wien's constant is 2.90 × 10⁻³ m K.

4. 4

   The Sun's spectrum peaks at 500 nm. Calculate its surface temperature.

   Model answer

   The temperature is T = (2.90 × 10⁻³) ÷ (500 × 10⁻⁹) = 5800 K. Multiplying 5800 K by 5.00 × 10⁻⁷ m returns 2.90 × 10⁻³ m K.

5. 5

   A star has a surface temperature of 10 000 K. Calculate the wavelength at which it radiates most strongly.

   Model answer

   The peak wavelength is λₘₐₓ = (2.90 × 10⁻³) ÷ 10 000 = 2.90 × 10⁻⁷ m, or 290 nm. Multiplying 2.90 × 10⁻⁷ m by 10 000 K returns 2.90 × 10⁻³ m K.

6. 6

   In which part of the electromagnetic spectrum does a star peaking at 290 nm radiate most strongly?

   Model answer

   It peaks in the ultraviolet, since 290 nm is shorter than the shortest visible wavelength.

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