Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 4, Problem 50P
To determine
Compare the wavelengths of the normal and redshifted spectral lines for the
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Of 1.5, 3, 5, and 10 give the maximum apparent speeds.
2. Consider a relativistic jet with an angle of 70 degrees relative to the line of sight (i.e. it is
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A gamma ray burst delivers approximately 1.0 X10-6 joules/m2 to a detector on an orbiting space telescope. Assuming that the red shift indicates that the source is 5 X109 light years away (1 yr =3.16X107 seconds) and that the energy at the detector has been corrected for the redshift, what is the energy output of the source and how does it compare to the rest energy of the Sun. The speed of light is 3.0 X 108 m/sec. A year is 3.16 X 107 sec. The mass of the Sun is 2 X 1030 kg. Rest mass energy is E=mc2. The surface area of a sphere is 4πr2.
Answer choices:
1.2 X1045joules and 0.7 %
8 X 1047 joules and 100%
5 X 1046 joules and 8%
2.8 X 1046 joules and 16%
In the mass function f(Ma, M) = MB/(1+ Ma/MB)² sin°i = M/(Ma + Mb) sin°i it gives us a lower limit on the mass of the unseen component of a single-lined
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Chapter 4 Solutions
Modern Physics for Scientists and Engineers
Ch. 4 - Prob. 1QCh. 4 - Prob. 2QCh. 4 - Prob. 3QCh. 4 - Prob. 4QCh. 4 - Prob. 5QCh. 4 - Prob. 6QCh. 4 - Prob. 7QCh. 4 - Prob. 8QCh. 4 - Prob. 9QCh. 4 - Prob. 10Q
Ch. 4 - Prob. 11QCh. 4 - Prob. 12QCh. 4 - Prob. 13QCh. 4 - Prob. 2PCh. 4 - Prob. 3PCh. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - What fraction of 5-MeV α particles will be...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Prob. 12PCh. 4 - Prob. 13PCh. 4 - Prob. 14PCh. 4 - Prob. 15PCh. 4 - Prob. 16PCh. 4 - Prob. 17PCh. 4 - Prob. 18PCh. 4 - Prob. 19PCh. 4 - Prob. 20PCh. 4 - Prob. 21PCh. 4 - Prob. 22PCh. 4 - Prob. 23PCh. 4 - Prob. 24PCh. 4 - Prob. 25PCh. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Prob. 33PCh. 4 - Prob. 34PCh. 4 - Prob. 35PCh. 4 - Prob. 36PCh. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Prob. 42PCh. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Prob. 46PCh. 4 - Prob. 47PCh. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - Prob. 50PCh. 4 - Prob. 51PCh. 4 - Prob. 52PCh. 4 - Prob. 54PCh. 4 - Prob. 55PCh. 4 - Prob. 56PCh. 4 - Prob. 57PCh. 4 - Prob. 59PCh. 4 - Prob. 60PCh. 4 - Prob. 61P
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- In vacuum, the H-alpha line has a rest-frame wavelength of 656.461 nm. You took a spectrum of the center of a galaxy at an observatory on the ground and measured a wavelength of 656.65 nm for the H-alpha line. What is the radial velocity of the galaxy relative to the observer [km/s]? Note that the index of refraction of air is 1.0003 at that wavelength. As a result, the rest-frame wavelength of the H-alpha line in air differs from the rest-frame wavelength in vacuum.arrow_forwardProblem 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.arrow_forwardGeneral Relativity Consider a spherical blackbody of constant temperature and mass M whose surface lies at radial coordinate r = R. An observer located at the surface of the sphere and a distant observer both measure the blackbody radiation given off by the sphere. If the observer at the surface of the sphere measures the luminosity of the blackbody to be L, use the gravitational time dilation formula, to show that the observer at infinity measures. 2GM L̟ = L] 1– Rcarrow_forward
- Suppose 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_forwarddouble line The velocity curve spectroscopic binary is shown in the sketch. The system is viewed edge-on, i.e., with an inclination angle of i = 90°, so that the maximum possible Doppler shifts for this system are observed. for a 400 So = U, Ani 300 200 no - V Ain i 100 -100 -200 -300 400 • 1 2 3 . S 6 7 8 10 Time (days) Find the mass ratio, m1/m2, of the stars. Express your answer as a fraction like a/b Doppler Velocityarrow_forwardEdwin Hubble observed that the light from very distant galaxies was redshifted and that the farther away a galaxy was, the greater its redshift. What does this say about very distant galaxies? When Hubble first estimated the Hubble constant, galaxy distances were still very uncertain, and he got a value for H of about 600 km/s per Mpc. What would this have implied about the age of the universe? What problems would this have presented for cosmologists?arrow_forward
- A star’s spectrum emits more radiation with a wavelength of 690.0 nm than with any other wavelength. If the star is 9.78 ly from Earth and its radius is 7.20 × 108 m, what will an Earth-based observer measure for this star’s intensity? Stars are nearly perfect blackbodies. (Note: ly stands for light-years.) Answer in W/m2arrow_forwardIf we were to analyze the magnetic flux lines of a current-carrying conductor, oriented perpendicularly to a magnetic field between two bar magnets, the interaction would look something like this: S N S N This interaction of magnetic flux lines (the bar magnets' straight lines versus the wire's cireles) will produce a mechanical force on the wire (called the Lorentz force). Which direction will this force act? Also, determine the direction of current through the conductor (seen from an end-view in the above illustration) necessary to produce the circular magnetic flux shown.arrow_forwardQuasars are faint, distant sources of radio waves. (Quasar is short for "quasi-stellar source." They are so named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the frequency of their emitted light toward the red, called the "redshift," we know that quasars are moving very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In this way they determine that quasars are billions of light years from earth. To be visible at this great distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the order of 1040 W, roughly 1014 times greater than the sun or 40 times greater than the most luminous galaxy. At what rate is rest mass being consumed to produce this much radiation?arrow_forward
- Quasars are faint, distant sources of radio waves. (Quasar is short for "quasi-stellar source." They are so named because, like a star, they appear to the astronomer to be pointlike.) From the shift in the frequency of their emitted light toward the red, called the "redshift," we know that quasars are moving very fast. Astronomers observe that the more distant an object is from the earth, the faster it moves. In this way they determine that quasars are billions of light years from earth. To be visible at this great distance, quasars must have enormous luminosity. Typically a quasar radiates energy at a rate on the order of 1040 W, roughly 1014 times greater than the sun or 40 times greater than the most luminous galaxy. At what rate is rest mass being consumed to produce this much radiation? Quasar 3C-273arrow_forwardNear the center of our galaxy, hydrogen gas is moving directly away from us in its orbit about a black hole. We receive electromagnetic radiation of wavelength 1908 nm and know that it was 1875 nm when emitted by the hydrogen gas.Randomized Variablesλ = 1908 nm What is the ratio of the speed of the gas to the speed of light?arrow_forwardAt rest, hydrogen has a spectral line at 124 nm. If this line is observed at 133 nm for the star Sirius, how fast is Sirius moving in km/s?arrow_forward
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