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.
Hi, can you please assist with C?
& For reference:
A = 0.0011 m
B = 1.807 x 10^-22 J
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.
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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- 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_forwardWhy is Hubble’s law considered one of the most important discoveries in the history of astronomy?arrow_forwardhttps://www.compadre.org/PQP/special-relativity/section2_4.cfm A) Look at the first animation. Change the value of Beta. What do you observe when betais 0.1 vs. when beta is 0.9?B) Look at the second animation. Change the value of Beta. What do you observe whenbeta is 0.1 vs. when beta is 0.9?arrow_forward
- 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 Кarrow_forwardTwo students in a science club argue with each other regarding the concept of Redshift. The statements made by the students are given as follows: Student 1: When the absorption maxima shift towards longer wavelengths then it is called the Redshift. Student 2: The decrease in wavelength due to the Doppler effect is known as the Redshift. Which of the above statement/s is/are correct? (a) Both student 1 and student 2 are true. (b) Only student 1 is true. (c) Only student 2 is true. (d) Both student 1 and student 2 are false.arrow_forwardAssuming stars to behave as black bodies stefan-boltzmann law to show that the luminosity of a star is related to its surface temperature and size in the following way: L = 4(3.14)R^2oT^4 where o= 5.67 ×10^-8 Wm^-2 K-4 is the stefan- boltzmann constant. Then use this expression together with the knowledge that the sun has a surface temperature of 5700k and radius 695 500km to calculate the luminosity of the Sun in units of Wattsarrow_forward
- A student wants to determine the Stefan-Boltzmann constant, o. The student then measures the 3) luminosity, surface area, and temperature of an object. The temperature of the object is changed several times. The student measures the new temperature and luminosity for each of the new cases. The surface area is assumed to be the same in each case. The data is then plotted to determine the Stefan-Boltzmann constant. The student knows that the relationship between these quantities is given by the Stefan-Boltzmann Law: L= GAT* (19) To determine the Stefan-Boltzmann constant we need to transform the data, that according to the theory will be a 4th degree polynomial, to form a straight line. How do we transform the data so that the graph will be linear? What is the slope of the line? What are the labels for the vertical and horizontal axis of the graph? Hint: Consider how we transformed the data in case 2 from a quadratic to linear.arrow_forwardE2arrow_forwardWhat is the most likely range of values for Hubble’s constant? What are the uncertainties in its value?arrow_forward
- What is the peak wavelength (in nm) of a neutron star's luminosity if its temperature is 106 K?arrow_forwardB9arrow_forwardIf you find that the Hubble constant is double what we currently believe, how does this affect the calculated age of the universe? Group of answer choices It decreased it by a factor of four. It cuts it in half. It doubles it. It increases it by a factor of four.arrow_forward
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