B

When an electron is accelerated through a potential difference of 1 volt, it gains a kinetic energy equal to the work done on it by the electric field. The work done (or energy gained) by a charge 'q' moving through a potential difference 'V' is given by the formula:
Work done (W) = q × V
For an electron, the charge 'q' is approximately equal to \( 1.6 \times 10^{-19} \) coulombs. Therefore, if the electron is accelerated through a potential difference of 1 volt, the energy gained is:
Energy = 1.6 \times 10^{-19} C \times 1 V = 1.6 \times 10^{-19} J
This amount of energy (1.6 x 10^-19 joules) corresponds to what is defined as 1 electron volt (eV). Hence, the kinetic energy acquired by an electron when it is accelerated through a potential difference of 1 volt is 1 electron volt. Therefore, the correct answer is B.