If a free electron moves through a potential difference of 1kV, then the energy gained by the electron is given by

The energy gained by a free electron when accelerated through a potential difference is calculated using the formula E = qV, where 'q' is the charge of the electron and 'V' is the potential difference. The elementary charge of an electron is approximately 1.6 × 10^-19 Coulombs. When an electron moves through a potential difference of 1 volt, it gains 1 electron-volt (eV) of energy, which is equivalent to 1.6 × 10^-19 Joules. In this case, the potential difference is 1 kV (1000 V). Therefore, the energy gained is (1.6 × 10^-19 C) × (1000 V) = 1.6 × 10^-16 Joules. This relationship between work done, charge, and potential difference is a fundamental principle of electrostatics.