problem_1 - ASTRONOMY 822 Electromagnetic Radiation Problem...

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Unformatted text preview: ASTRONOMY 822 Electromagnetic Radiation Problem Set 1 due Wednesday, October 5 at class time 1) If you could construct a box opaque to neutrinos, then at a temperature T , the thermal neutrinos inside the box would have the specific intensity I ( T ) = 2 h 3 /c 2 exp( h/kT ) + 1 . (Note the difference from the Planck distribution for photons; this results from the fact that neutrinos are fermions and photons are bosons). a) Find the frequency max at which the peak of I occurs, as a function of T . If T = 10 12 K (a temperature which can be reached in a collapsing Type II supernova core), what is the numerical value of max for neutrinos? b) Show that the energy density of neutrinos in the opaque box has the form u ( T ) = a T 4 . What is the value of a in terms of k , h , and c ? If T = 10 12 K, how large a box of neutrinos would you need to have a total neutrino energy of E = 10 53 erg? (This is the typical energy radiated in neutrinos from a Type II supernova.) 2) a) Approximate the Sun as a blackbody with a temperature of...
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problem_1 - ASTRONOMY 822 Electromagnetic Radiation Problem...

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