An electron moves at a speed of 0.8 of the speed of light. Determine the mass of the electron

An electron moves at a speed of 0.8 of the speed of light. Determine the mass of the electron, the rest energy of the electron, the total energy of the electron, the kinetic energy of the electron.

1) m = m0 / √ (1 – (v² / c²)) = m0 / √ (1 – ((0.8c) ² / c²);

m = 9.1 * 10-31 / √ (1 – (0.8² / 1)) = 1.5 * 10-30 kg.

2) E0 = m0 * c2;

E0 = 9.1 * 10-31 + (3 * 108) 2 = 8.2 * 10-14 J.

3) E = E0 / √ (1 – (v² / c²)) = E0 / √ (1 – ((0.8c) ² / c²));

E = 8.2 * 10-14 / √ (1 – (0.8² / 1)) = 1.37 * 10-13 J.

4) We find the kinetic one from the law of conservation of energy

E = Ek + E0;

Ek = E – E0;

Ek = 1.37 * 10-13 – 8.2 * 10-14 = 5.5 * 10-14 J.

Answer: 1.5 * 10-30 kg; 8.2 * 10-14 J; 1.37 * 10-13 J; 5.5 * 10-14 J.