
Concept explainers
(a)
The radial velocity of a star which has a wavelength of
(a)

Answer to Problem 10Q
Solution:
Explanation of Solution
Given data:
The wavelength of
Formula used:
Write the expression for radial velocity of the star.
Here,
Write the expression for the difference in the value of wavelength of
Here,
Explanation:
The change in the observed wavelength of the spectrum of a star moving away from or moving closer to an observer is a perfect example of redshift observed due to the Doppler’s effect.
Write the expression for the difference in the values of wavelength of
Substitute the values of
Recall the mathematical expression for the radial velocity of a star.
Substitute the values of
Conclusion:
Hence, the radial velocity of the star is
(b)
If a star is moving away or moving closer to an observer. It is given that the oberved value of the wavelength of
(b)

Answer to Problem 10Q
Solution:
The star is moving towards the observer.
Explanation of Solution
Given data:
The oberved value of the wavelength of
Explanation:
The value of the radial velocity of the star is calculated in the part (a) as
Conclusion:
Hence, the star is coming closer to the observer.
(c)
The observed value of the wavelength of the
(c)

Answer to Problem 10Q
Solution:
Explanation of Solution
Given data:
The laboratory value of the wavelength of
Formula used:
Write the expression for the radial velocity of a star.
Here,
Write the expression for the difference in the values of the wavelength of
Here,
Explanation:
Use the radial velocity of the star calculated in part (a) and use the mathematical expression to calculate the value of redshift to calculate the change in the wavelength of
Rewrite the mathematical expression for the radial velocity of a star.
Rearrange the above expression for
Substitute the known values of
Recall the mathematical expression for the difference in the value of the wavelength of
Rearrange the above expression for
Substitute the known values of
Conclusion:
Hence, the observed value of the wavelength of
(d)
If the caluclated value of the wavelength of
(d)

Answer to Problem 10Q
Solution:
The calculated value of the wavelength of
Explanation of Solution
Given data:
The laboratory value of
Explanation:
The observed spectrum of a star depends only on the relative motion of the observer and the star. The distance between these two does not play any role in the Doppler Effect.
Conclusion:
Hence, the value of the observed wavelength calculated does not depend on the distance between the star and the Sun.
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