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