# Calculate the wavelength problem

## 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.

## 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?

## Answers and Replies

Shooting Star
Homework Helper
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.)