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Electrons are accelerated through a voltage difference of 210 kV inside a high voltage accelerator tube....

Electrons are accelerated through a voltage difference of 210 kV inside a high voltage accelerator tube. What is the final kinetic energy of the electrons?

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What is the speed of these electrons in terms of the speed of the light? (Remember that the electrons will be relativistic.)

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Answer #1

Here , for the kinetic energy of electrons

kinetic energy of electrons = VOltage * e

kinetic energy of electrons = 210 * 10^3e

kinetic energy of electrons = 210 * 10^3 * 1.602 * 10^-19

kinetic energy of electrons = 3.36 *10-14 J

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let the speed of electron is v

kinetic energy = m * c^2 - m0 * c^2

3.36 *10^-14 = 9.11 * 10^-11 * (3 *10^8)^2 *(1/sqrt(1 - (v/c)^2) - 1)

solving for v

v = 0.705c

the speed of the electron is 0.705c

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