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6 June, 15:22

Calculate the speed (in m/s) of an electron and a proton with a kinetic energy of 1.85 electron volt (eV). (The electron and proton masses are me = 9.11 ✕ 10-31 kg and mp = 1.67 ✕ 10-27 kg. Boltzmann's constant is kB = 1.38 ✕ 10-23 J/K.)

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  1. 6 June, 19:18
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    ve = 8.06 x 10^5 m/s

    vp = 1.882 x 10^4 m/s

    Explanation:

    K = 1.85 eV = 1.85 x 1.6 x 10^-19 J = 2.96 x 10^-19 J

    me = 9.11 ✕ 10^-31 kg,

    mp = 1.67 ✕ 10^-27 kg

    Let the speed of electron is ve and the proton is vp.

    For electron:

    K = 1/2 me x ve^2

    2.96 x 10^-19 = 0.5 x 9.11 x 10^-31 x ve^2

    ve^2 = 6.498 x 10^11

    ve = 8.06 x 10^5 m/s

    For proton:

    K = 1/2 mp x vp^2

    2.96 x 10^-19 = 0.5 x 1.67 x 10^-27 x vp^2

    vp^2 = 3.5449 x 10^8

    vp = 1.882 x 10^4 m/s
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