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20 November, 11:03

A hydrogen atom contains a single electron that moves in a circular orbit about a single proton. Assume the proton is stationary, and the electron has a speed of 7.5 105 m/s. Find the radius between the stationary proton and the electron orbit within the hydrogen atom.

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  1. 20 November, 11:26
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    450 pm

    Explanation:

    The electron is held in orbit by an electric force, this works as the centripetal force. The equation for the centripetal acceleration is:

    a = v^2 / r

    The equation for the electric force is:

    F = q1 * q2 / (4 * π * e0 * r^2)

    Where

    q1, q2: the electric charges, the charge of the electron is - 1.6*10^-19 C

    e0: electric constant (8.85*10^-12 F/m)

    If we divide this force by the mass of the electron we get the acceleration

    me = 9.1*10^-31 kg

    a = q1 * q2 / (4 * π * e0 * me * r^2)

    v^2 / r = q1 * q2 / (4 * π * e0 * me * r^2)

    We can simplify r

    v^2 = q1 * q2 / (4 * π * e0 * me * r)

    Rearranging:

    r = q1 * q2 / (4 * π * e0 * me * v^2)

    r = 1.6*10^-19 * 1.6*10^-19 / (4 * π * 8.85*10^-12 * 9.1*10^-31 * (7.5*10^5) ^2) = 4.5*10^-10 m = 450 pm
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