Modern Physics, 3rd Edition
Modern Physics, 3rd Edition
3rd Edition
ISBN: 9780534493394
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
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Question
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Chapter 16, Problem 6P

(a)

To determine

Wavelength of light emitted from a galaxy lies at 2×106lightyears from the earth.

(a)

Expert Solution
Check Mark

Answer to Problem 6P

Wavelength is 590.2nm.

Explanation of Solution

Write the Hubble’s law equation.

    v=H0R        (I)

Here, v is the speed of galaxy, H0 is the Hubble’s constant and R is the distance from earth.

Write the relativistic doppler formula.

  λ=1+v/c1v/cλ        (II)

Here, λ is the observed wavelength and λ is the original wavelength.

Conclusion:

Substitute (2.3×102m/s)/ly for H0 and 2×106lightyears for R in equation (I).

    v=((2.3×102m/s)/ly)(2×106lightyears)=4.6×104m/s

Substitute 590 nm for λ, 4.6×104m/s for v and 3×108m/s for c in equation (II).

    λ=1+[(4.6×108m/s)/(3×108m/s)]1[(4.6×108m/s)/(3×108m/s)](590nm)=(1.00031)(590nm)=590.2nm

Thus, the wavelength is 590.2nm.

(b)

To determine

Wavelength of light emitted from a galaxy lies at 2×108lightyears from the earth.

(b)

Expert Solution
Check Mark

Answer to Problem 6P

Wavelength is 599.1nm.

Explanation of Solution

Substitute (2.3×102m/s)/ly for H0 and 2×108lightyears for R in equation (I).

    v=((2.3×102m/s)/ly)(2×108lightyears)=4.6×106m/s

Substitute 590 nm for λ, 4.6×106m/s for v and 3×108m/s for c in equation (II).

    λ=1+[(4.6×108m/s)/(3×108m/s)]1[(4.6×108m/s)/(3×108m/s)](590nm)=(1.015)(590nm)=599.1nm

Conclusion:

Thus, the wavelength is 599.1nm.

(b)

To determine

Wavelength of light emitted from a galaxy lies at 2×109lightyears from the earth.

(b)

Expert Solution
Check Mark

Answer to Problem 6P

Wavelength is 688.6nm.

Explanation of Solution

Substitute (2.3×102m/s)/ly for H0 and 2×109lightyears for R in equation (I).

    v=((2.3×102m/s)/ly)(2×109lightyears)=4.6×107m/s

Substitute 590 nm for λ, 4.6×107m/s for v and 3×108m/s for c in equation (II).

    λ=1+[(4.6×109m/s)/(3×108m/s)]1[(4.6×109m/s)/(3×108m/s)](590nm)=(1.16)(590nm)=688.6nm

Conclusion:

Thus, the wavelength is 688.6nm.

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