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A star at a temperature of 8200 K is observed in a distant galaxy at redshift = 2.7.(i) Which equation relates the observed wavelength, to the actual wavelength, , emitted by the star? Select the correct option from the following.

Question

A star at a temperature of 8200 K is observed in a distant galaxy at redshift = 2.7.(i) Which equation relates the observed wavelength, to the actual wavelength, , emitted by the star? Select the correct option from the following.

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Solution

The equation that relates the observed wavelength (λ_observed) to the actual wavelength (λ_emitted) emitted by the star is given by the equation for redshift (z), which is:

1 + z = λ_observed / λ_emitted

This equation is derived from the Doppler effect, which describes how the frequency of a wave changes for an observer moving relative to the source of the wave. In the context of astronomy, redshift happens when light or other electromagnetic radiation from an object is increased in wavelength, or shifted to the red end of the spectrum. In this case, the star is moving away from the observer, causing the light to be "stretched", increasing the wavelength and shifting the light to the red end of the spectrum.

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