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4 March, 11:10

What is the wavelength of light that is emitted when an excited electron in the hydrogen atom falls from n = 5 to n = 1?

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  1. 4 March, 11:39
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    9.49 x 10⁻⁸ m

    Explanation:

    Data given:

    excitation of electron = n-5 to n-1

    wavelength of light = ?

    Solution:

    As the transition of electron take place from one level to other so the problem will be solved by using Rydberg's equation

    Rydberg's equation

    1/λ = R [1/n² (final) - 1/n² (initial) ]

    where

    R = Rydberg's constant = 1.0974 x 10⁷ m⁻¹

    λ = wavelength

    n (final) = the final energy level

    n (initial) = the initial energy level

    Now

    Put the values in Rydberg's equation

    1/λ = R [1/n² (final) - 1/n² (initial) ]

    1/λ = 1.0974 x 10⁷ m⁻¹ (1/1² - 1/5²)

    1/λ = 1.0974 x 10⁷ m⁻¹ (1/1 - 1/25)

    1/λ = 1.0974 x 10⁷ m⁻¹ (1 - 0.04)

    1/λ = 1.0974 x 10⁷ m⁻¹ (0.96)

    1/λ = 1.0535 x 10⁷ m⁻¹

    λ = 1 / 1.0535 x 10⁷ m⁻¹

    λ = 9.49 x 10⁻⁸ m

    the wavelength of light that is emitted = 9.49 x 10⁻⁸ m
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