By Kevin Beck | Updated August 30, 2022

Electrons are one of the three fundamental building blocks of atoms, alongside protons and neutrons. Each electron has a mass of 9 × 10⁻³¹ kg and carries a negative elementary charge of 1.6 × 10⁻¹⁹ C. When an electron enters an electric field, the field’s potential difference accelerates it much like gravity accelerates a projectile.

Step 1: Choose the Correct Energy Equation

In classical mechanics, kinetic energy is ½ mv². For charged particles in an electric field, the work done by the field equals the kinetic energy gained:

q V = ½ m v²

Here, m = 9 × 10⁻³¹ kg, and q = 1.6 × 10⁻¹⁹ C.

Step 2: Identify the Potential Difference

Voltage is the electric potential difference between two points in the field. An electron (negative charge) moves from low to high potential (toward the positive electrode), gaining kinetic energy proportional to the voltage drop.

Step 3: Solve for the Electron’s Speed

Rearranging the energy equation gives the speed:

v = √(2 q V / m)

For example, if the electron accelerates across a 100 V potential difference:

v = √(2 × 1.6 × 10⁻¹⁹ C × 100 V / 9 × 10⁻³¹ kg) = 6 × 10⁶ m/s.

Thus, a 100‑volt field propels an electron to roughly six million meters per second—about 2 % of light speed. Knowing this relationship is essential for designing electron microscopes, particle accelerators, and many other applications in physics and engineering.