When the light from a distant galaxy is analysed, it is found that a line on its spectrum is 32 nm longer than when the same spectrum is produced on Earth. Given that the light was emitted with a wavelength of 430 nm, calculate the cosmic scale factor when it was emitted. Give your answer to 2 significant figures.
Question
When the light from a distant galaxy is analysed, it is found that a line on its spectrum is 32 nm longer than when the same spectrum is produced on Earth. Given that the light was emitted with a wavelength of 430 nm, calculate the cosmic scale factor when it was emitted. Give your answer to 2 significant figures.
Solution
The cosmic scale factor is calculated by dividing the observed wavelength by the emitted wavelength.
In this case, the observed wavelength is the emitted wavelength plus the change in wavelength due to the expansion of the universe.
So, the observed wavelength is 430 nm (emitted wavelength) + 32 nm (change in wavelength) = 462 nm.
Therefore, the cosmic scale factor is 430 nm / 462 nm = 0.93 (to 2 significant figures).
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