In a terrestrial laboratory three prominent spectral lines i

In a terrestrial laboratory, three prominent spectral lines in the optical portion of the spectrum emitted by excited hydrogen gas are at 656.3 nm, 486.1nm and 410.2 nm. When analyzing the spectrum from a distant galaxy, we observe those same hydrogen lines at the wavelengths of 659.6nm, 488.5nm, and 412.3 nm. Is the galaxy approaching or receding from the earth? At what speed? A rocketship traveling at 0.1c fires a green laser beam (tambda = 550 nm) along the direction of its velocity. What is the wavelength of the laser as detected by an observer on an asteroid?

Solution

a. As there is an increase in the wavelength the object is moving away from us and thus we are observing the wavelengths shift towards a redshift.
b. (lambda - lambda_not)*c / lambda = velocity
So, (659.6-656.3)*3*(10^8)/656.3 = 1508341 m/s
c. v = 3*10^7
(lambda - (550*10^-9))/(550*10^-9)=.1
lambda = 605 nm