Question

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?

Answer 1

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

Explanation:

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