PHYS 3022
Introduction to Cosmology
Spring 2014
Homework Solutions Week 2
Problem 1
Note: be careful not to make the mistake
λ
peak
=
c/
ν
peak
. The distribution of black body
radiation (Planck’s Law) as a function of frequency has a di
ff
erent shape than the distri
bution as a function of wavelength. To find the peak of each function (Planck equation
for frequency or wavelength), you must apply calculus of variation (take derivative and
set to 0) to the Planck equation for each function. This question asks you to find the
peak intensity
wavelength
for the CMB.
Thus, in answering (a) and (b), using the wavelength form of Wien’s Law:
λ
m
≈
hc
kT
×
0
.
201405
,
then the result is 1
.
1mm for the CMB and 5
.
0
×
10
3
˚
A for the Sun.
For (a) and (b), if you used the frequency form of Wien’s Law, and then erroneously
converted to wavelength via
λν
=
c
you would see that in fact you would get di
ff
erent
answers than above.
h
ν
m
kT
≈
2
.
822
and using
λ
m
=
c
ν
m
,
then the result is 1
.
9mm for the CMB and 8
.
8
×
10
3
˚
A for the Sun.
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 Spring '14
 Hanany
 Energy, Work, Radiation, North Pole, South Pole, CMB, CMB photons

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