An electron moves from one plate of a capacitor to another t

An electron moves from one plate of a capacitor to another, through a potential difference of 5.000 V. Proton Mass = 1.67 times 10^-27kg and Electron Mass = 9.11 times 10^-31 kg) Find the speed with which the electron strikes the positive plate. If a proton moves from the positive plate to the negative plate. find the speed with which the proton strikes the negative plate.

Solution

Here ,

V = 5000 V

mp = 1.67 *10^-27 Kg

me = 9.11 *10^-31 Kg

a)

let the speed of electron is v

Using conservation of energy

0.5 * m * v^2/sqrt(1- (v/c)^2) = q * V

0.5 * 9.11 *10^-31 * v^2/sqrt(1- (v/(3 *10^8))^2) = 5000 * 1.602 *10^-19

solving for v

v = 4.17 *10^7 m/s

the speed of electron is 4.17 *10^7 m/s

b)

let the speed of proton is v

0.5 * m * v^2/sqrt(1- (v/c)^2) = q * V

0.5 * 1.67 *10^-27 * v^2/sqrt(1- (v/(3 *10^8))^2) = 5000 * 1.602 *10^-19

solving for v

v = 9.79 *10^5 m/s

the speed of proton is 9.79 *10^5 m/s