Unformatted text preview: enominator in the Planck Function in the long and short wavelength limits.]
6. [C&O 3.10] A comparison of RayleighJeans to Planck’s function.
a. Show that the RayleighJeans law (Eq. 3.20) is an approximation of the
Planck function Bλ. (Eq. 3.22) in the limit of λ»hc/kT. (The firstorder
expansion ex~1+x for x«1 will be useful.) Notice that Planck's constant is
not present in your answer. The RayleighJeans law is a classical result, so
the “ultraviolet catastrophe” at short wavelengths, produced by the λ4 in
the denominator, cannot be avoided.
b. Plot the Planck function Bλ and the RayleighJeans law for the Sun (Te =
5777 K) on the same graph. At roughly what wavelength is the RayleighJeans value twice as large as the Planck function?
7. [C&O 3.11 (tweaked)] Show that Wien's expression for blackbody radiation (Eq.
3.21) follows directly from Planck's function (Eq. 3.22) at short wavelengths.
8. [C&O 3.13 (tweaked)] Examining the Planck function in terms of frequency...
a. Use Eq. (3.24) to show that the fr...
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This document was uploaded on 03/04/2014 for the course ASTROPHYS 362 at Minnesota State University Moorhead .
 Spring '14
 Dr.JuanCabanela

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