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11 November, 05:45

A diatomic molecule is rotating about its center of mass with an angular speed of 2.50 ✕ 1012 rad/s. Determine the rotational kinetic energy (in J) of one molecule, if the gas is fluorine which has a bond length of 0.919 Å and a molecular molar mass of 38.0 g/mole.

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  1. 11 November, 09:10
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    Answer: kinetic energy Ke = 4.16 * 10^-22J

    Explanation:

    Moment of inertia I = 2mr^2

    m = (38 * 10^-3 kg/mol) / (2 * 6.02 * 10^23)

    Atomic mass m = 3.16 * 10^-26 kg

    r = bond length/2 = 0.919Å/2 = 0.4595Å

    Bond radius r = 0.4595 * 10^-10m

    I = 2 * 3.16*10^-26 * (0.4595 * 10^-10) ^2

    I = 1.33 * 10^-46 kgm^2

    Kinetic energy Ke = 1/2 (I * w^2)

    Angular speed w = 2.50 ✕ 10^12 rad/s

    Ke = 1/2 (1.33 * 10^-46 kgm^2 * (2.5 * 10^ 12rad/s) ^2)

    Ke = 4.16 * 10^-22J
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