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4 December, 23:07

A relativistic proton has a momentum of 1.0 * 10-19 kg · m/s and a rest energy of 0.15 nJ. What is the kinetic energy of this proton? (c = 3.00 * 108 m/s, mproton = 1.67 * 10-27 kg)

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  1. 5 December, 00:01
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    The kinetic energy is 0 J.

    Explanation:

    The kinetic energy of a relativistic proton is determined as follows:

    KE = mc² - m₀c²

    To determine m₀, we use the expression

    E_rest = m₀c²

    where

    E_rest is the rest energy c is the speed of light m₀ is the rest mass

    Thus, rearranging the above expression we get

    m₀ = E_rest/c²

    = (0.15*10⁻⁹) / (3*10⁸) ²

    = 1.67*10⁻²⁷ kg

    Therefore,

    KE = (1.67*10⁻²⁷) (3*10⁸) ² - (1.67*10⁻²⁷) (3*10⁸) ²

    = 0 J
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