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14 December, 21:29

An excited hydrogen atom emits light with a wavelength of 486.4 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin?

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  1. 14 December, 21:49
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    The electron began in the quantum level of 4

    Explanation:

    Using the formula of wave number:

    Wave Number = 1/λ = Rh (1/n1² - 1/n2²)

    where,

    Rh = Rhydberg's Constant = 1.09677 x 10^7 / m

    λ = wavelength of light emitted = 486.4 nm = 486.4 x 10^-9 m

    n1 = final shell = 2

    n2 = initial shell = ?

    Therefore,

    1/486.4 x 10^-9 m = (1.09677 x 10^7 / m) (1/2² - 1/n2²)

    1/4 - 1 / (486.4 x 10^-9 m) (1.09677 x 10^7 / m) = 1/n2²

    1/n2² = 0.06082

    n2² = 16.44

    n2 = 4
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