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What speed should a galaxy move with respect to us so that the sodium line at  \(589\;\text{nm}\) is observed at \(589.6\;\text{nm}\) ?

Answer

Given data,
Initial wavelength  \(\lambda _0=589\;\text{nm}\)
Final wavelength  \(\lambda =589.6\;\text{nm}\)
 \({\Delta}\lambda =589.6-589=0.6\;\text{nm}\) 
We know by Doppler’s effect,
 \(\frac{-{\Delta}\lambda }{\lambda _0}=\frac{-v} C\) 
Where,  \({\Delta}\lambda =\) shift in wavelength, \(v=\) speed of galaxy,  \(C=\) speed of light
Putting values, we get,
 \(v=3.06\times 10^5\left(\frac m s\right)\) 
 \(v=306\;\mathit{km}/ s\)  
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