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4 February, 07:12

In the Bohr model of hydrogen, the electron moves in a circular orbit around the nucleus. (a) Determine the orbital frequency of the electron when it is in the ground state. rev/s (b) Determine the orbital frequency of the electron when it is in the first excited state.

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  1. 4 February, 09:04
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    (a) 6.567 * 10^15 rev/s or hertz

    (b) 8.21 * 10^14 rev/s or hertz

    Explanation:

    Fn = 4π^2k^2e^4m * z^2 / (h^3*n^3)

    Where Fn is frequency at all levels of n.

    Z = 1 (nucleus)

    e = 1.6 * 10^-19c

    m = 9.1 * 10^-31 kg

    h = 6.62 * 10-34

    K = 9 * 10^9 Nm2/c2

    (a) for groundstate n = 1

    Fn = 4 * π^2 * (9*10^9) ^2 * (1.6*10^-19) ^4 * (9.1 * 10^-31) * 1 / (6.62 * 10^-31) ^3 = 6.567 * 10^15 rev/s

    (b) first excited state

    n = 1

    We multiple the groundstate answer by 1/n^3

    6.567 * 10^15 rev/s / 2^3

    F2 = 8.2 * 10^ 14 rev/s
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