Thermionic Emission (Edexcel International A Level Physics)

Electron guns use electric fields to accelerate electrons to very high speeds.

Show that an electron accelerated from rest across a potential difference of 5.0 kV attains a speed of 4.2 × 10⁷ m s^–1. 

Use the following data: 

• Mass of an electron m_e = 9.11 × 10^–31 kg

• Electron charge e = 1.6 × 10^–19 C

Answer:

Step 1: List the known quantities

• Potential difference = 5 kV = 5000 V

• Mass of an electron, m_e = 9.11 × 10^–31 kg

• Electron charge e = 1.6 × 10^–19 C

Step 2: Equate the kinetic energy gained by the electron to the energy transferred across the potential difference

• Potential difference V is the energy transferred W per unit of charge Q, or 

• Since the charge in this case is an electron, Q = e and so W = eV

• Therefore, the kinetic energy gained is equal to eV so we can write:

Step 3: Make speed v the subject of the equation

• Rearranging this equation for v gives:

Step 4: Substitute quantities and calculate the speed v

• Substituting known quantities gives:

= 41 908 313... = 4.2 × 10⁷ m s^–1

Examiners commonly test if candidates can equate the energy gained across a potential difference with the kinetic energy of a particle, as we did here. Make sure you can combine the equations for kinetic energy and potential energy in order to calculate speed like we did here!