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19 January, 09:31

According to Bohr's theory, what is the frequency of the light emitted by an electron in a transition from the first excited state to the ground state in hydrogen? Compare this with the frequency of the orbital motion of the electron in the first excited state.

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  1. 19 January, 09:55
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    frequency transition 2.4626 10¹⁵ Hz

    Explanation:

    Bohr's atomic model works very well for the hydrogen atom, the energy of the states is described by the expression

    En = - 13.606 / n² eV

    Where n is a positive integer

    Let's calculate the energy for the base state n = 1 E1 = - 13.606 eV

    The energy for the first excited state n = 2 E2 = - 13.6060 / 2²

    E2 = - 3.4015 Ev

    The variation of the energy for the transition is

    ΔE = E2 - E1

    ΔE = - 3.4015 + 13.606

    ΔE = 10.2045 eV

    We use the Planck equation to find the frequency

    E = 10.2045 eV (1.6 10⁻¹⁹ J/1 eV) = 16.3272 10⁻¹⁹ J

    E = h f

    f = E / h

    f = 16.3272 10⁻¹⁹ / 6.63 10⁻³⁴

    f = 2.4626 10¹⁵ Hz

    Let's calculate the frequency of the excited state

    E2 = 3.4015 eV (1.6 10⁻¹⁹ J/1eV) = 5.4424 10⁻¹⁹ J

    f = 5.4424 10⁻¹⁹ / 6.63 10⁻³⁴

    f = 0.8209 10¹⁵ Hz

    To make the comparison, divide the two frequencies

    f transition / f excited = 2.4626 / 0.8209

    f transition / f excited = 3

    The frequency of the transition is 3 times greater than the frequency of the first excited state
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