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omegas

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## Homework Statement

Starting with the Planck distribution R([tex]\lambda[/tex],T) for blackbody radiation.

(a) Derive the blackbody Stefan-Boltzmann law (ie total flux is proportional to T

^{4}) by integrating the above expression over all wavelengths. Thus show that

**R(T) = (2[tex]\pi[/tex]**

^{5}k^{4})T^{4}/ (15h^{3}c^{2}(b) Show that the maximum value of R([tex]\lambda[/tex],T) occurs for [tex]\lambda[/tex]

_{m}T = 2.898 * 10

^{-3}mK (this is called Wien's displacement law).

(c) Use Wien's displacement law to determine for the cosmic background radiation with T = 2.7 K

(i) the value of [tex]\lambda[/tex]

_{m}for peak intensity

(ii) the energy in eV of photons at this peak intensity, and

(iii) the region of the electromagnetic spectrum corresponding to the peak intesnsity.

## Homework Equations

Planck distribution for blackbody radiation:

**R([tex]\lambda[/tex],T) = (c/4)(8[tex]\pi[/tex]/[tex]\lambda[/tex]**

^{4}[(hc/[tex]\lambda[/tex])1/e^{hc/[tex]\lambda[/tex]kT}-1]## The Attempt at a Solution

That was a mouthful. Help please.