The lifetime of quasar.

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Chapter 19, Problem 39QP

To determine

The lifetime of quasar.

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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.

An astronomical image shows two objects that have the same apparent magnitude, i.e., the same brightness. However, spectroscopic follow up observations indicate that while one is a star that is within our galaxy, at a distance dgal away, and has the same luminosity as the Sun, the other is a quasar and has 100x the luminosity of the entire Milky Way galaxy. What is the distance to the quasar? (You may assume, for this rough calculation, that the Milky Way has 1011 stars and that they all have the luminosity as the Sun.) Give your response in Mpc. Value: dgal = 49 pc

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