Wavelengths of light from a distant galaxy are found to be 0.5% longer than the corresponding wavelengths measured in a terrestrial laboratory. At what speed is the galaxy receding?

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Answer 1 · 2016-03-10T03:24:27

Speed at Which the Galaxy is moving = 1492.537313432836 km /sec

Red-Shift = ( $Lambda_"L"$ - $Lambda_"O"$ )/ $Lambda_"O"$

Here,

$Lambda_"O"$ is the Observed Wavelength.
$Lambda_"L"$ is the Wavelength measured in a Laboratory.

Now the Observed wavelength is 0.5% longer than the wavelength measured in a Lab.

$Lambda_"O"$ = 0.005 * $Lambda_"L"$ + $Lambda_"L"$

Red_shift = ( $Lambda_"L"$ - (0.005 * $Lambda_"L"$ + $Lambda_"L"$ ))/ (0.005 * $Lambda_"L"$ + $Lambda_"L"$ )

Red_shift = ( $Lambda_"L"$ - 0.005 $Lambda_"L"$ - $Lambda_"L"$ ))/ ((1.005 $Lambda_"L"$ ))

Red_shift =-0.004975

Speed = Red-Shift * Speed of Light.

Speed = 0.004975 * 300000 km /sec

Speed at Which the Galaxy is moving = 1492.537313432836 km /sec