Question

Electrons are accelerated through a voltage difference of 170 kV inside a high voltage accelerator tube. What is the final kinetic energy of the electrons? Tries 0/20 Submit Answer What is the speed of these electrons in terms of the speed of the light? (Remember that the electrons will be relativistic.) Submit Answer Tries 0/20

Answer 1

Potential difference V = 170000 V

Kinetic energy of the electrons

K = Vq

q = 1.6 x 10 ^-19 C

so ,

K = 2.72 x 10 ^-14 J

(b).Speed of electron v = ?

We know K = m ' c ² - m c ²

Where m = mass of electron

               = 9.11 x 10 ^-31 kg

          m ' = relativistic mass

                = m / √[1-(v/c) ² ]

K / c ² = m ' - m

          = [m / √[1-(v/c) ² ]] - m

         = m {[ 1 / √[1-(v/c) ² ] - 1}

K / mc ² = {[ 1 / √[1-(v/c) ² ] - 1}

0.3317 = {[ 1 / √[1-(v/c) ² ] - 1}

{[ 1 / √[1-(v/c) ² ] } = 1.3317

√[1-(v/c) ² ] = 0.7508

[1-(v/c) ² ] =0.5638

              v = 0.564 c