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Homework 2 Solution - PHYS 3022 Introduction to Cosmology...

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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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