Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
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Chapter 2, Problem 102P
Quasars are among the most distant objects in the universe and are moving away from us at very high speeds, as discussed in Chapter 16. Astrophysicists use the redshift parameter z to determine the redshift of such rapidly moving objects. The parameter z is determined by observing a wavelength λ′ of a known spectral line of wavelength λsource on Earth; z = Δλ/λsource = (λ′ − λsource) /λsource. Find the speed of two quasars having z values of 1.9 and 4.9.
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The bright radio galaxy, 3c84, is observed to be moving away from the Earth at such high speed that the emitted blue 434-nm Hγ line of hydrogen is Doppler-shifted to 442 nm.
Edwin Hubble discovered that all objects outside the local group of galaxies are moving away from us, with speeds v proportional to their distances R. Hubble's law is expressed as v = HR, where the Hubble constant has the approximate value
H ≈ 22 ✕ 10−3 m/(s · ly).
Determine the distance from the Earth to this galaxy. _________ ly
Name:
Hubble Distances
Redshift z parameter
The relativistic redshift is parametrized by z and given by
Δ
In terms of the scale factor,
2=
X
do - de
de
1+z=
ao
a
(2)
Problem 01. Find the redshift z for a Hydrogen spectral line originally at 656 nm which
has been observed at a wavelength of 1.64 μm.
Astro 001 Fall 2022
Problem 02. How much smaller was the universe when this light was emitted?
U₁ = DHO
Using the redshift to measure the velocity, we find
D~
(1)
0.1 Hubble's Law
Hubble's Law states that the recession velocity of a redshifted galaxy is given by the product
of the distance and the Hubble constant.
(3)
ZC
Ho
where c = 3 x 108 m/s and Ho = 2.3 x 10-18 s in standard units. The standard measurement
of the Hubble constant is Ho = 71 (km/s)/Mpc.
Problem 03. What is the distance in Mpc and ly to the galaxy measured in problem 01?
1 pc = 3.26 ly.
The spectral lines of various elements are detected in light from a galaxy in the constellation Ursa Major. An ultraviolet line from singly ionized calcium (lS = 393 nm) is observed at wavelength l0 = 414 nm, redshifted into the visible portion of the spectrum. At what speed is this galaxy receding from us?
Chapter 2 Solutions
Modern Physics for Scientists and Engineers
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