The Cosmic Perspective (9th Edition)
The Cosmic Perspective (9th Edition)
9th Edition
ISBN: 9780134874364
Author: Jeffrey O. Bennett, Megan O. Donahue, Nicholas Schneider, Mark Voit
Publisher: PEARSON
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Chapter S3, Problem 60EAP

Gravitational Time Dilation on the Sun. Use the formula given in Problem 59 to calculate the percentage by which time runs slower on the surface of the Sun than in deep space. Based on your answer, approximately how much of a gravitational redshift should you expect for a spectral line with a rest wavelength of 121.6 nm?

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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 Lorentz force causes charged particles to orbit around magnetic field lines. At what rate do protons orbit around a field line? Assume the protons have energy of 1 MeV and are in a magnetic field with strength B = 2.4×10-7 T. Find the orbital frequency in revolutions/second (Hz); express your answer to 3 significant digits. The protons orbit the field at _____ Hz.   How would the answer to the previous problem change if the particles were 1 MeV electrons, instead of protons?
The following quotation is taken from the article “Quantum Black Holes”, by Bernard J. Carr and Steven B. Giddings, in the May 2005 issue of Scientific American. "The total time for a black hole to evaporate away is proportional to the cube of its initial mass. For a solar-mass hole, the lifetime is an unobservably long 1064 years." a. Recall that the solar mass is 2 × 10³0 kilograms. Write a formula for the lifetime, L, of a black hole as a function of its mass, m. Start by finding the value of the constant k, then write your function using the letter k (rather than its value in scientific notation). For example, for a direct variation you would write “L(m) = km”. k = a × 10¹ where a = L(m) = b. The present age mass = c × 10ª kg, where c = A and b = = of the universe is about 10¹0 years. What would be the mass of a black hole as old as the universe? ID and d = J

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The Cosmic Perspective (9th Edition)

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