If light from a galaxy observed on the earth's surface has a red shift,then:

What speed (in $km/s$) should a galaxy move with respect to us so that the sodium line at $589.0 \;nm$ is observed at $589.6 \;nm$?

$A$ star moves away from the Earth at a speed of $0.8\,c$ while emitting light of frequency $6 \times 10^{14} \,Hz$. What frequency will be observed on the Earth? ($c =$ speed of light)

$A$ star producing light of wavelength $6000 \ \mathring{A}$ moves away from the Earth with a speed of $5 \ km/s$. Due to the Doppler effect, the shift in wavelength will be $...... \ \mathring{A}$ $(c = 3 \times 10^8 \ m/s)$.

When the wavelength of light coming from a distant star is measured,it is found to be shifted towards the red end of the spectrum. What is the conclusion?

If the velocity of a galaxy relative to the Earth is $1.2 \times 10^6 \, m/s$,then the percentage increase in the wavelength of light from the galaxy as compared to a similar source on Earth will be ...............$\%$