What is the observed wavelength of the 656.3 nm (first Balmer) line of hydrogen emitted by a galaxy at a distance of 2.40 x 108 ly

Question

What is the observed wavelength of the 656.3 nm (first Balmer) line of hydrogen emitted by a galaxy at a distance of 2.40 x 108 ly

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Delwyn 1 month 2021-08-07T20:00:18+00:00 1 Answers 3 views 0

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    2021-08-07T20:01:52+00:00

    Answer:

    λ = 667.85 nm

    Explanation:

    Let f be the frequency detected by the observer

    Let v be the speed at which the observer is moving.

    Now, when the direction at which the observer is moving is away from the source, we have the frequency as;

    f = f_o√((1 – β)/(1 + β))

    From wave equations, we know that the wavelength is inversely proportional to the frequency. Thus, wavelength is now;

    λ = λ_o√((1 + β)/(1 – β))

    Where, β = Hr/c

    H is hubbles constant which has a value of 0.0218 m/s • ly

    c is speed of light = 3 × 10^(8) m/s

    r is given as 2.40 x 10^(8) ly

    Thus,

    β = (0.0218 × 2.4 x 10^(8))/(3 × 10^(8))

    β = 0.01744

    Since we are given λ_o = 656.3 nm

    Then;

    λ = 656.3√((1 + 0.01744)/(1 – 0.01744))

    λ = 667.85 nm

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