Question

One of the strongest emission lines observed from distant galaxies comes from hydrogen and has a wavelength of 122 nm (in the ultraviolet region). (a) How fast must a galaxy be moving away from us in order for that line to be observed in the visible region at 366 nm

Answer 1

Answer:

$v=2.4*10^8m/s$

Explanation:

From the question we are told that

Wavelength of emission $\lambda=122nm$

Observation distance $d=366nm$

Generally the s equation is given as

$f'=f\sqrt{\frac{(1-\frac{v}{c} )}{1+\frac{v}{c} }$

where

F is inversely proportional to T

$d=\lambda\sqrt{\frac{(1-\frac{v}{c} )}{1+\frac{v}{c} }$

$\frac{v}{c} =\frac{(1-\frac{\lambda}{d})}{(1+\frac{\lambda}{d}}$

$\frac{v}{c}=\frac{1-(\frac{122}{366} )^2}{1+(\frac{122}{366})^2}$

$\frac{v}{c}=\frac{0.8888888889}{1.11111111}$

$\frac{v}{c}=0.80$

$v=0.80*3*10^6$

$v=2.4*10^8m/s$