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Homework Statement
By direct calculation, derive and expression for the wavelength λ(max) at which blackbody radiation intensity is a maximum
2. Homework Equations
Planck's law for the intensity distribution of blackbody radiation as a function of wavelength λ and the blackbody temperature T is given by
I(λ,T) = (2pi)hc^2/(λ^5)(e^((hc)/λkT) -1)
h is Planck's constant 6.626 x10^(-34)
k is blotzman constant 1.38066 x10^(-23)
c is speed of light
The Attempt at a Solution
(-5(2pi)(hc^2)λ^(-6))/(e^(hc)/(λkT) - 1) + λ^(-5)(2pi)(hc^2)(-1)(e^((hc)/(λkT)) -1)^(-2)((-hc)/(kTλ^2))
I used the product rule to get to the answer. I have not yet simplified I am wondering if I have even started the problem correctly.