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Energy density in cavity radiation as a function of frequency

2. The sun radiates approximately as a black body or a cavity radiator at 5800 K.
a) Find the frequency at which the energy density is maximum as a function of
frequency,
b) Find the wavelength at which the energy density is a maximum as a function of
wavelength.
c) Find the frequencya t which the photond ensityi s a maximuma sa functiono f
frequency.

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(a)
Energy per unit volume per unit frequency of a blackbody radiation is

S = 2π(kT)^3/(c^2h^2) * x^3/(e^x-1), (1)

where x = hf/(kT)

As the energy of a photon is hf, the number of photons per unit volume per unit frequency is
N = S/(hf) = 2π(kT)^2/(c^2h^2) * x^2/(e^x-1) (2)

1(b)
Its maximum is when dN/dx = 0. Differentiating equation (2) we obtain the ...

Solution Summary

This solution answers questions addressing frequency, wavelength and energy density

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