The electron began to move from a state of rest and passed the accelerating potential difference of 80 V.

The electron began to move from a state of rest and passed the accelerating potential difference of 80 V. The electron charge is 1.6 * 10 ^ -19 C. what speed has the electron acquired? Take the mass of an electron equal to 9.0 * 10 ^ -31.

V0 = 0 m / s.

U = 80 V.

q = 1.6 * 10 ^ -16 Cl.

m = 9 * 10 ^ -31 kg.

V -?

The electric field performs the mechanical work of accelerating the electron. According to the law of conservation of energy, the work of the electric field A is equal to the change in the kinetic energy of the electron ΔEk: A = ΔEk.

The work of the electric field A on the movement of the electric charge and the change in the kinetic energy of the electron ΔEk are expressed by the formulas: A = q * U, ΔEk = Ek – Ek0 = m * V ^ 2/2 – m * V0 ^ 2/2 = m * V ^ 2 / 2.

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

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

V = √ (2 * q * U / m).

V = √ (2 * 1.6 * 10 ^ -16 C * 80 V / 9 * 10 ^ -31 kg) = 1.68 * 10 ^ 7 m / s.

Answer: from a state of rest, the electron will accelerate to a speed of V = 1.68 * 10 ^ 7 m / s.