How can Wien's Displacement Law be 'changed' to a version for frequency? Wien's Displacement Law s

arbixerwoxottdrp1l

arbixerwoxottdrp1l

Answered question

2022-05-09

How can Wien's Displacement Law be 'changed' to a version for frequency?
Wien's Displacement Law stated that for a blackbody emitting radiation,
λ m a x = 1 T
where T is the temperature of the body and λ m a x is the maximum wavelength of radiation emitted.
Due to the relationship between wavelength, frequency and the speed of light, a value of maximum wavelength would give a value of minimum frequency, and vice versa.
I then saw on the Wikipedia page for Wien's Displacement Law that
f m a x = α k B T h ,
where α = 2.82..., k B is Boltzmann's Constant, T is the temperature of the body and h is Planck's Constant.
How can this relationship for maximum frequency be shown?

Answer & Explanation

necrologo9yh43

necrologo9yh43

Beginner2022-05-10Added 23 answers

The Wien displacement law gives the maximum of a function, so the way to compute it is to start with the Planck function in frequency domain,
B ( ν , T ) = 8 π ν 2 c 3 h ν e h ν / k T 1
Take the derivative with respect to ν, set it equal to zero and solve for ν. You'll likely have to use some numerical methods (e.g., iterative searching) to find the value.

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