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22 April, 11:47

A Physicists often use a different unit of energy, the electron volt, when dealing wth e electron volt, abbreviated eV, is defined as the amount of kinetic energy gained by an electron upon accelerating through a 1.0 V potential difference. What is 1.0 electron volt in joules? at the atomic level. What is the speed of a proton with 2500 eV of kinetic energy? Express your answer with the appropriate units.

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  1. 22 April, 15:13
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    Answer: 1ev = 1.609*10^-19 J

    velocity of electron = v = 2.97 * 10^7 m/s

    Explanation: The magnitude of an electronic charge (e) is given as

    e = 1.609*10^-19c

    The amount of kinetic energy an electron has when it moves through 1v equals the work done used in accelerating the electron (according to work - energy theorem).

    K. E = W = eV

    e = magnitude of electron = 1.609 * 10^-19c

    V = 1v

    Hence 1ev = 1.609 * 10^-19 * 1

    1ev = 1.609 * 10^-19 J.

    If K. E = 2500ev.

    By converting this to joules we have that

    If 1ev = 1.609 * 10^-19 J.

    Then 2500ev = 1.609 * 10^-19 * 2500

    K. E (in joules) = 4005 * 10^-19

    K. E = 4.005 * 10^-16 J.

    But K. E = 1/2mv²

    Where K. E = kinetic energy of electron = 4.005 * 10^-16 J.

    m = mass of electronic charge = 9.11 * 10 ^-31kg.

    By substituting the parameters, we have that

    4.005 * 10^-16 = 1/2 * 9.11 * 10 ^-31 * v²

    4.005 * 10^-16 * 2 = 9.11 * 10 ^-31 * v²

    8.01 * 10^-16 = 9.11 * 10^-31 * v²

    v² = 8.01 * 10^-16 / 9.11 * 10^-31

    v² = 0.879 * 10^15

    v² = 8.79 * 10^14

    v = √8.79 * 10^14

    v = 2.97 * 10^7 m/s
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