Unformatted text preview: enominator in the Planck Function in the long and short wavelength limits.]
6. [C&O 3.10] A comparison of Rayleigh-Jeans to Planck’s function.
a. Show that the Rayleigh-Jeans law (Eq. 3.20) is an approximation of the
Planck function Bλ. (Eq. 3.22) in the limit of λ»hc/kT. (The first-order
expansion ex~1+x for x«1 will be useful.) Notice that Planck's constant is
not present in your answer. The Rayleigh-Jeans 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 Rayleigh-Jeans 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