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13 May, 23:34

In a simple model of the Hydrogen atom, an electron moves in uniform circular motion with a speed of 2.2 x 106 m/s around a proton. (a) Determine the radius of the electron's orbit. (b) Find the centripetal acceleration of the electron in this orbit.

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  1. 13 May, 23:37
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    a) Radius of electron' s orbit = 5.29 * 10⁻¹¹ m

    b) Centripetal Acceleration, α = 9.15 * 10²² m/s²

    Explanation:

    The force of attraction between a proton and an electron of the simple model of Hydrogen atom is obtained from literature to be 8.325 * 10⁻⁸ N

    It is this force that is driving the the circular motion of the electron. Centripetal force is given by

    F = mv²/r

    r = mv²/F

    m = mass of the electron = 9.11 * 10⁻³¹ kg

    v = velocity of the electron = 2.2 * 10⁶ m/s

    r = 9.11 * 10⁻³¹ * (2.2 * 10⁶) ² / (8.325 * 10⁻⁸)

    r = 5.29 * 10⁻¹¹ m

    b) centripetal acceleration, α = F/m or v²/r

    α = (8.325 * 10⁻⁸) / (9.11 * 10⁻³¹) = (2.2 * 10⁶) ² / (5.29 * 10⁻¹¹) = 9.15 * 10²² m/s²
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