The discussion centers on the concept of monochromatic energy density (Uλ) of blackbody radiation, specifically its dependence on wavelength (λ) and temperature (T). The correct relationship is established as U(λ) ∝ λ-5, indicating that monochromatic energy density is inversely proportional to the fifth power of wavelength. This contrasts with the total energy density, which follows the Stefan-Boltzmann law and is proportional to T4. The confusion arises from the distinction between monochromatic and total energy density.
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Abdul Quadeer said:Homework Statement
Monochromatic energy density (Uλ)(i.e., per unit volume) of the radiation of
a blackbody is proportional to (where λ is wavelength)
(1) T4
(2) λ -5
(3) λ5/2
(4) T5/4The Attempt at a Solution
A slight modification of Stefan-Boltzmann's law suggests that the answer should be (1), but the answer given is (2). Is my book wrong?
The problem refers to " monochromatic energy density" and is thus asking about the energy density per unit wavelength.
G01 said:If you integrate that over all possible wavelengths, you get the energy density (energy/volume) which has the temperature dependence you expect.