Calculate the wavelength problem

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To calculate the observed wavelength of ultraviolet radiation from hydrogen in a receding galaxy, the relativistic Doppler effect formula is applied due to the galaxy's speed of 0.11c. The formula for frequency adjustment is f' = f*sqrt[(c-v)/(c+v)], where f is the source frequency and v is the relative speed. This approach accounts for the redshift caused by the galaxy's motion away from the observer. While the expansion of the Universe contributes to redshift, the special relativistic formula is adequate for this velocity. The discussion emphasizes the importance of using the correct formula to find the observed wavelength accurately.
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Homework Statement


The wavelength of a particular ultraviolet radiation from hydrogen atoms is 1.216 e-7 m. Calculate the wavelength when the corresponding radiation from hydrogen in a distant galaxy is observed here on earth. The galaxy is receding at a speed of 0.11 c.


Homework Equations





The Attempt at a Solution


I'm not sure what to do with the "receding at a speed of .11c" to solve this problem.. suggestions?
 
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When there is relative motion between the light or EM source and the observer, and the relative speed is high, the relativistic Doppler effect formula has to be used. The simplest case is when the motion is directly away from each other with a relative speed of v. If the frequency of the source in its rest frame is f, then the the observer will measure the frequency of the radiation as f' = f*sqrt[(c-v)/(c+v)].

Receding at a speed of .11c means that the relative velocity is 0.11c away from each other.

(To be very correct, the galaxies show redshift because of the expansion of the Universe, but the special relativistic formula will suffice for a relative speed of 0.11c.)
 
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