The correct answer is option 2: 1.6 X 10-16 J.

When a free electron moves through a potential difference, it gains energy. The energy gained by an electron can be calculated using the formula E = qV, where E is the energy gained, q is the charge of the electron, and V is the potential difference.

The charge of an electron is approximately 1.6 X 10-19 C. The potential difference given in the question is 1kV, which is equivalent to 1000 V.

Substituting the values into the formula, we get E = (1.6 X 10-19 C) × (1000 V) = 1.6 X 10-16 J.

Therefore, the energy gained by the electron when it moves through a potential difference of 1kV is 1.6 X 10-16 J.

Note: Option 1 (1.6 X 10-19 J) and option 3 (1 X 10-19 J) are incorrect as they do not match the correct value. Option 4 (1 X 10-16 J) is also incorrect as it does not match the correct value of 1.6 X