Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 21, Problem 51Q
To determine
The difference between gamma ray and X-ray bursts and the reason for X-ray bursts to emit repeated pulses, whereas gamma ray bursts emit just once.
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1.2
1.0
0.8
0.6
Cosmic background
data from COBE
0.4
0.2
0.0
0.5
10
Wavelength A in mm
c)
Background (CMB) undertaken by the COBE satellite. Use this diagram to estimate the
current temperature of the CMB. Based on your estimate, what would the temperature of
the CMB have been at a redshift of z = 5000?
The left hand diagram above shows the results from observations of the Cosmic Microwave
Radiated Intensity per Unit Wavelength
(16° Watts/m per mm)
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.
Imagine that you are observing the light from a distant star that is located in a galaxy 100 million lightyears
away from you. By analysis of the starlight received, you are able to tell that the image we see is of a 10-
million-year-old star. You are also able to predict that the star will have a total lifetime of 50 million years, at
which point it will end in a catastrophic supernova.
a) How old does the star appear to be to us here on Earth now?
b) How long will it be before we receive the light from the supernova event?
c) Has the supernova already occurred? If so, when did it occur?
Chapter 21 Solutions
Universe: Stars And Galaxies
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- In the Check Your Learning section of Example 27.1, you were told that several lines of hydrogen absorption in the visible spectrum have rest wavelengths of 410 nm, 434 nm, 486 nm, and 656 nm. In a spectrum of a distant galaxy, these same lines are observed to have wavelengths of 492 nm, 521 nm, 583 nm, and 787 nm, respectively. The example demonstrated that z=0.20 for the 410 nm line. Show that you will obtain the same redshift regardless of which absorption line you measure.arrow_forwardHi, can you please assist with C? & For reference: A = 0.0011 m B = 1.807 x 10^-22 Jarrow_forwardGiven a 10 Jy source with an occupying 15'' in the sky, at a distance of 1.1 Mpc, observed at 1.4 GHz, determine the brightness temperature of the source.arrow_forward
- How much energy could we obtain from 1 kg of hydrogen if it were to undergo nuclear fusion in the interior of a star? The proton mass is 1.00794 amu and the Helium mass is 4.002602 amu. Please please show all calculations and what numbers you are using thank you i will give a thumbs uparrow_forwardThe 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.arrow_forwardWhat is thought to cause the higher-energy gamma-ray bursts, which do not appear to repeat?arrow_forward
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