Calculate the wavelength problem

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SUMMARY

The discussion focuses on calculating the observed wavelength of ultraviolet radiation from hydrogen atoms in a distant galaxy receding at a speed of 0.11c. The relativistic Doppler effect formula is essential for this calculation, specifically f' = f*sqrt[(c-v)/(c+v)], where f is the frequency in the rest frame and v is the relative speed. The original wavelength of the radiation is given as 1.216 e-7 m, and the redshift due to the galaxy's recession must be accounted for to determine the observed wavelength on Earth.

PREREQUISITES
  • Understanding of the relativistic Doppler effect
  • Familiarity with the speed of light (c)
  • Knowledge of wavelength and frequency relationships
  • Basic concepts of redshift in astrophysics
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  • Learn how to calculate redshift and its implications in cosmology
  • Explore the relationship between wavelength and frequency in electromagnetic radiation
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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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