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Chapter 31, Problem 41P

(a)

To determine

The wavelength of the sodium line emitted from galaxies.

(a)

Expert Solution
Check Mark

Answer to Problem 41P

The wavelength of the sodium line emitted from galaxies is 590.09nm_.

Explanation of Solution

Write the expression for velocity from Hubble’s law.

v=HR        (I)

Here, v is the velocity, H is the Hubble’s constant and R is the distance.

Write the expression for the wavelength by using equation (I).

λ'=λ1+(v/c)1(v/c)=λ1+(HR/c)1(HR/c)        (II)

Here, λ is the observed velocity and λ is the given wavelength.

Conclusion:

Substitute, 22×103m/s.ly for H, 2.00×106ly for R, 2.998×108m/s for c, 590nm for λ in equation (II) to find λ.

λ'=(590nm)1+((22×103m/s.ly)(2.00×106ly)/(2.998×108m/s))1((22×103m/s.ly)(2.00×106ly)/(2.998×108m/s))=590.09nm

Thus, the wavelength of the sodium line emitted from galaxies is 590.09nm_.

(b)

To determine

The wavelength of the sodium line emitted from galaxies.

(b)

Expert Solution
Check Mark

Answer to Problem 41P

The wavelength of the sodium line emitted from galaxies is 599nm_.

Explanation of Solution

Write the expression for velocity from Hubble’s law.

v=HR        (I)

Here, v is the velocity, H is the Hubble’s constant and R is the distance.

Write the expression for the wavelength by using equation (I).

λ'=λ1+(v/c)1(v/c)=λ1+(HR/c)1(HR/c)        (II)

Here, λ is the observed velocity and λ is the given wavelength.

Conclusion:

Substitute, 22×103m/s.ly for H, 2.00×108ly for R, 2.998×108m/s for c, 590nm for λ in equation (II) to find λ.

λ'=(590nm)1+((22×103m/s.ly)(2.00×108ly)/(2.998×108m/s))1((22×103m/s.ly)(2.00×108ly)/(2.998×108m/s))=599nm

Thus, the wavelength of the sodium line emitted from galaxies is 599nm_.

(c)

To determine

The wavelength of the sodium line emitted from galaxies.

(c)

Expert Solution
Check Mark

Answer to Problem 41P

The wavelength of the sodium line emitted from galaxies is 684nm_.

Explanation of Solution

Write the expression for velocity from Hubble’s law.

v=HR        (I)

Here, v is the velocity, H is the Hubble’s constant and R is the distance.

Write the expression for the wavelength by using equation (I).

λ'=λ1+(v/c)1(v/c)=λ1+(HR/c)1(HR/c)        (II)

Here, λ is the observed velocity and λ is the given wavelength.

Conclusion:

Substitute, 22×103m/s.ly for H, 2.00×109ly for R, 2.998×108m/s for c, 590nm for λ in equation (II) to find λ.

λ'=(590nm)1+((22×103m/s.ly)(2.00×109ly)/(2.998×108m/s))1((22×103m/s.ly)(2.00×109ly)/(2.998×108m/s))=684nm

Thus, the wavelength of the sodium line emitted from galaxies is 684nm_.

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Chapter 31 Solutions

Bundle: Principles of Physics: A Calculus-Based Text, 5th + WebAssign Printed Access Card for Serway/Jewett's Principles of Physics: A Calculus-Based Text, 5th Edition, Multi-Term

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