Question Details An electron is accelerated inside a parallel plate capacitor. T

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Question Details
An electron is accelerated inside a parallel plate capacitor. The electron leaves the negative plate with a negligible initial velocity and then after the acceleration it hits the positive plate with a final velocity ß. The distance between the plates is 13.5 cm, and the voltage difference is 113 kV.

a) Determine the final velocity ß of the electron using classical mechanics. (The rest mass of the electron is 9.11×10-31 kg, the rest energy of the electron is 511 keV.)

b)What is the final velocity ß of the electron if you use relativistic mechanics?

Explanation / Answer

d = 0.135 m, V = 113 kV, m = 9.11×10-31 kg, rest energy E0 = 511 keV, charge q = e

a) kinetic energy K = qV = 113 keV = mv2/2 = m(c)2/2 = 2E0/2

= (2E/E0) = 0.665

b) K = mc2/(1 - 2) - mc2

1/(1 - 2) = 1 + K/E0 = 1.2211

= 0.574

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