Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 16, Problem 42QAP
To determine
The peak wavelength of the CMB spectrum; find temperature of the CMB by Wien’s law; the calculated temperature compared to the accepted temperature.
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Problem 2: Black hole – the ultimate blackbody
A black hole emits blackbody radiation called Hawking radiation. A black hole with mass
M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of
hc³/167²KGM.
a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar
mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole.
b) Calculate the total power radiated by a one-solar mass black hole.
c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing.
As it loses energy, its mass must decrease; one could say "evaporates". Derive a
differential equation for the mass as a function of time, and solve to obtain an
expression for the lifetime of a black hole in terms of its mass.
The Andromeda Galaxy, M31, is the closest large spiral galaxy to our Milky Way. When we look at its chemical spectrum, we see that its hydrogen alpha emission line (Hα) has an observed wavelength of λobs = 655 nm.-Calculate z, being careful with the sign.-How fast is it moving in km/s?-Is it redshifted or blueshifted? Is it moving towards or away from us?
answer to three significant figures.
The temperature of the CMB today is
T=2.725 K. Calculate the temperature of
the CMB at redshift z=2000. Choose the
option below that most closely matches
your answer.
Select one:
O a. 9759 K
O b. 3412 K
Ос.
5453 K.
O d. 5450K
Ое. 2000 К
Chapter 16 Solutions
Understanding Our Universe
Ch. 16.1 - Prob. 16.1CYUCh. 16.2 - Prob. 16.2CYUCh. 16.3 - Prob. 16.3CYUCh. 16.4 - Prob. 16.4CYUCh. 16.5 - Prob. 16.5CYUCh. 16.6 - Prob. 16.6CYUCh. 16 - Prob. 1QAPCh. 16 - Prob. 2QAPCh. 16 - Prob. 3QAPCh. 16 - Prob. 4QAP
Ch. 16 - Prob. 5QAPCh. 16 - Prob. 6QAPCh. 16 - Prob. 7QAPCh. 16 - Prob. 8QAPCh. 16 - Prob. 9QAPCh. 16 - Prob. 10QAPCh. 16 - Prob. 11QAPCh. 16 - Prob. 12QAPCh. 16 - Prob. 13QAPCh. 16 - Prob. 14QAPCh. 16 - Prob. 15QAPCh. 16 - Prob. 16QAPCh. 16 - Prob. 17QAPCh. 16 - Prob. 18QAPCh. 16 - Prob. 19QAPCh. 16 - Prob. 20QAPCh. 16 - Prob. 21QAPCh. 16 - Prob. 22QAPCh. 16 - Prob. 24QAPCh. 16 - Prob. 25QAPCh. 16 - Prob. 26QAPCh. 16 - Prob. 27QAPCh. 16 - Prob. 28QAPCh. 16 - Prob. 29QAPCh. 16 - Prob. 30QAPCh. 16 - Prob. 31QAPCh. 16 - Prob. 32QAPCh. 16 - Prob. 33QAPCh. 16 - Prob. 34QAPCh. 16 - Prob. 35QAPCh. 16 - Prob. 36QAPCh. 16 - Prob. 37QAPCh. 16 - Prob. 38QAPCh. 16 - Prob. 39QAPCh. 16 - Prob. 40QAPCh. 16 - Prob. 41QAPCh. 16 - Prob. 42QAPCh. 16 - Prob. 43QAPCh. 16 - Prob. 44QAPCh. 16 - Prob. 45QAP
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