Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Chapter 16, Problem 9P
To determine
The temperature of the system .
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Use Wien’s law to answer the following questions: (a) The cosmic background radiation peaks in intensity at a wavelength of 1.1 mm. To what temperature does this correspond? (b) About 379 000 y after the big bang, the universe became transparent to electromagnetic radiation. Its temperature then was 2970 K.What was the wavelength at which the background radiation was then most intense?
The geometry of spacetime in the Universe on large scales is determined by the mean energy density of the matter in the Universe, ρ. The critical density of the Universe is denoted by ρ0 and can be used to define the parameter Ω0 = ρ/ρ0. Describe the geometry of space when: (i) Ω0 < 1; (ii) Ω0 = 1; (iii) Ω0 > 1. Explain how measurements of the angular sizes of the hot- and cold-spots in the CMB projected on the sky can inform us about the geometry of spacetime in our Universe. What do measurements of these angular sizes by the WMAP and PLANCK satellites tell us about the value of Ω0?
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.
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- The photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today’s universe 1.00 m on a side, with a volume of 1.00 m3. What was the length s0 of each side and the volume V0 of this same cubical region 380,000 years after the Big Bang? s0 = ? m V0 = ? m^3 Today the average density of ordinary matter in the universe is about 2.4×10−27 kg/m3. What was the average density ?(rho)0 of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? (rho)0 = ? kg/m^3arrow_forwardAstronomers can determine the heat of various areas of the universe by making observations about energy they emit. Gamma rays can be found in areas where there is a lot of star formation occurring. What would you guess about the temperature of these areas? Explain why.Do you think there would be a lot of particles present? Explain why.arrow_forwardSuppose a star 1000 times brighter than our Sun (that is, emitting 1000 times the power) suddenly goes supernova. Using data from Table: (a) By what factor does its power output increase? (b) How many times brighter than our entire Milky Way galaxy is the supernova? (c) Based on your answers, discuss whether it should be possible to observe supernovas in distant galaxies. Note that there are on the order of 1011 observable galaxies, the average brightness of which is somewhat less than our own galaxy.arrow_forward
- 1. The current (critical) density of our universe is pe = 10-26kg/m³. Assume the universe is filled with cubes with equal size that each contain one person of m = 100kg. What would the length of the side of such a cube have to be in order to give the correct critical density? How many hydrogen atoms would you need in a box of 1 m³ to reach the critical density? The matter we know, which consists mostly of hydrogen, constitutes only 4.8% of the current critical energy density of our universe. So how many hydrogen atoms are actually in a box of 1 m3 in our universe? Deep space is very empty and a much better vacuum than we can obtain on earth in a laboratory.arrow_forwardI asked the following question and was given the attached solution: Suppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3) I don't follow the work and I got the wrong answer, so please help and show your work as I do not follow along easily thanksarrow_forwardEach second, an atom clock runs 0.0006 second slower than usual. This clock and a normal clock start running side by side. After 3 days, how much slower would the slower clock run compared to the normal clock? After 3 days, the slower clock would be ??? seconds slower than the normal clock. (Don’t round your answer.)arrow_forward
- Assuming 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_forwardSince you are made mostly of water, you are very efficient at absorbing microwave photons. If you were in intergalactic space, how many CMB photons would you absorb per second? (The assumption that you are spherical will be useful.) What is the rate, in watts, at which you would absorb radiative energy from the CMB?arrow_forwardThe photons that make up the cosmic microwave background were emitted about 380,000 years after the Big Bang. Today, 13.8 billion years after the Big Bang, the wavelengths of these photons have been stretched by a factor of about 1100 since they were emitted because lengths in the expanding universe have increased by that same factor of about 1100. Consider a cubical region of empty space in today's universe 1.00 m on a side, with a volume of 1.00 m³. What was the length so of each side and the volume V of this same cubical region 380,000 years after the Big Bang? So = Vo = Enter numeric value Today the average density of ordinary matter in the universe is about 2.4 × 10-27 kg/m³. What was the average density po of ordinary matter at the time that the photons in the cosmic microwave background radiation were emitted? Po = m m³ kg/m³arrow_forward
- Suppose the Universe is dominated by a strange substance with an equation of state w = -0.7. This substance fills the Universe in a uniform way, and is the only dynamically important constituent. Suppose further that in some time interval the Universe doubles in (linear) size, i.e. the scale factor doubles. By what factor has the energy density of this substance changed during this time interval, i.e., what is εfinal/εinitial? The energy density substance dilutes in proportion to a to some power p, i.e. ε(a) ∝ aparrow_forwardThe time before which we don’t know what happened in the universe (10-43 s) is called the Planck time. The theory needed is a quantum theory of gravity and concerns the three fundamental constants h, G, and c. (a) Use dimensional analysis to determine the exponents m, n, l if the Planck time tP = hmGncl . (b) Calculate the Planck time using the expression you found in (a).arrow_forwardSuppose that the universe were full of spherical objects, each of mass m and radius r . If the objects were distributed uniformly throughout the universe, what number density (#/m3) of spherical objects would be required to make the density equal to the critical density of our Universe? Values: m = 4 kg r = 0.0407 m Answer must be in scientific notation and include zero decimal places (1 sig fig --- e.g., 1234 should be written as 1*10^3)arrow_forward
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