Determine the modulus of the speed at which the electrons reach the anode in the vacuum diode

Determine the modulus of the speed at which the electrons reach the anode in the vacuum diode if the voltage between the anode and cathode is 200 V.

m = 9.1 * 10 ^ -31 kg.

q = 1.6 * 10 ^ -19 Cl.

U = 220 V.

V0 = 0 m / s.

V -?

The work of the electric field A goes to increase the kinetic energy of the electron ΔEk: A = ΔEk.

The work of the electric field on the movement of the electron A is expressed by the formula: A = q * U, where q is the charge of the electron, U is the voltage that it has passed.

The kinetic energy of an electron Ek is determined by the formula: Ek = m * V ^ 2/2, where m is the mass of the electron, V is the speed of its movement.

ΔEk = Ek – E0 = m * V ^ 2/2 – m * V0 ^ 2/2 = m * V ^ 2/2.

q * U = m * V ^ 2/2.

V = √ (2 * q * U / m).

V = √ (2 * 1.6 * 10 ^ -19 C * 220 V / 9.1 * 10 ^ -31 kg) = 8.8 * 10 ^ 6 m / s.

Answer: electrons reach the anode with a speed of V = 8.8 * 10 ^ 6 m / s.