The Electronvolt The e V is a useful

The Electronvolt

The e. V is a useful unit when working in particle physics because it makes the calculations and answers more convenient to handle: instead of dealing with the small numbers in terms of joules its simpler to work in the e. V.

The electronvolt is the energy acquired when one electron accelerates through a potential difference of 1 V. The work done by the electric field is found from the equation W = QV This is changed from electrical work to kinetic energy, EK, by conservation of energy. 1 electronvolt = 1. 6 x 10 -19 C x 1 V 1 e. V = 1. 6 x 10 -19 J. Often the unit Me. V is used; 1 Me. V = 1. 6 x 10 -13 J.

Examples 1. An electron is accelerated through a voltage of 2. 5 k. V. What is the energy gained by the electron. Express your answer in electron volts. Answer: W = QV = 1. 6 x 10 -19 x 2500 = 4 x 10 -19 J If 1 e. V = 1. 6 x 10 -19 J 4 x 10 -19 = 4 x 10 -19 / 1. 6 x 10 -19 = 2500 e. V (Note that for a single electron the answer in e. V is same numerically as the voltage. )

2. An ion with a charge of 3 e is accelerated until its energy is 0. 054 Me. V. What is the accelerating voltage? Answer 1 e. V = 1. 6 x 10 -19 J 1 Me. V = 1. 6 x 10 -13 J 0. 054 Me. V = 0. 054 x 1. 6 x 10 -13 J W =QV 0. 054 x 1. 6 x 10 -13 = 3 x 1. 6 x 10 -19 x V V = 18000 V

In Particle physics the mass is sometimes quoted in e. V. Show that the mass of an electron is 0. 51 Me. V.

E = mc 2 0. 51 x 106 x 10 -19 = m x (3 x 108)2 m = 9. 1 x 10 -31 kg