12.1.2 Thermionic Emission

Application of Thermionic Emission: Electron Guns

An electron gun is a device that utilises thermionic emission to produce a stream of electrons. Here's how it works:

1. Heating the Cathode: The metal cathode is heated to induce thermionic emission, releasing electrons from its surface.
2. Acceleration of Electrons: Once emitted, these electrons are accelerated towards a positively charged anode due to a potential difference (voltage) applied between the cathode and anode.
3. Electron Beam Formation: Electrons passing through a small gap in the anode form a narrow beam that moves at a constant velocity beyond the anode, resulting in a focused stream of electrons.

Work Done on a Charged Particle

The work done on an electron in an electric field can be calculated by:

$$\Delta W = eV$$

Where:

• $e$ is the charge on an electron (approximately 1.6 × 10^-19 C).
• $V$ is the potential difference through which the electron is accelerated. This equation shows the relationship between the work done on the electron and the potential difference it experiences.

Measuring Energy in Electron Volts (eV)

The energy gained by an electron is often measured in electron volts (eV), where 1 eV represents the kinetic energy of an electron accelerated across a potential difference of 1 V.

Energy Transformation in the Electron Gun

As an electron moves from the cathode towards the anode, its electrical potential energy is converted into kinetic energy. This means the electron gains speed as it travels. By the time it reaches the anode, the electron's kinetic energy equals the work done on it by the electric field:

$$\frac{1}{2}mv^2 = eV$$

Where:

• $m$ is the mass of the electron,
• $v$ is the final velocity of the electron. This equation helps to determine the speed of electrons after they are accelerated by the electron gun.