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7 December, 03:17

How much kinetic energy does a proton gain if it is accelerated, with no friction, through a potential difference of 1.00 V? The proton is 1836 times heavier than an electron

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  1. 7 December, 03:45
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    If energy is conserved, then the sum of the potential energy and the kinetic energy is a constant.

    Assuming the proton starts from rest, so it's kineitc energy is zero, but it has a potential energy, PE equal to:

    PE = qV

    where q = 1.6 x 10^-19 C

    and V = 1.00 V

    Assuming the proton no longer experiences the potential energy and it is all converted to kinetic energy then:

    PE * = 0,

    KE * = 1 / (2mv^2)

    Now since

    PE + KE = Total energy = PE * + KE*

    Therefore,

    qV + 0 = 0 + 1/2mv^2

    Or

    KE = qV = 1.6 10^-19 J
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