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,
\(v=3.06\times 10^5\left(\frac m s\right)\)
\(v=306\;\mathit{km}/ s\)
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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