Derive the Wiens displacement law max T= (hc)/(4.965 k) from the Planck blackbody radiation equation

Derive the Wien’s displacement law

λ _max T= (hc)/(4.965 k)

from the Planck blackbody radiation equation

μ = [( 8 π hc)/ λ ⁵ ] [1/ (e ^hc/λkt – 1)]

You will have to use a method of successive approximations to obtain the value 4.965.

Arrange your final result so that (hc)/ (λ _max kT) is on one side. Then assume that

e- ^hc/λkt , as it appears on the other side, is << 1.

This should lead to a value of 5 for the constant instead of 4.965. Repeated use of the constant (beginning with 5 ) in the full expression should converge to the proper value.

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