Thermionic Electron Emission

Rutherford-Bohr model of the atom

Electrons in an atom are in a state of constant motion, each possessing its own kinetic energy as they orbit the nucleus at the atom's centre. The Rutherford-Bohr model of the atom, as proposed by Niels Bohr and Ernest Rutherford in the early 20th century, states that the orbit of each of these electrons is dependent on their particular kinetic energies, with electrons of higher kinetic energy orbiting further from the centre of the atom.

The discrete levels at which these electrons orbit are known as energy levels, counting out from the atom's centre. An electron in an atom may go up an energy level if it gains kinetic energy, or go down an energy level if it loses kinetic energy. The Rutherford-Bohr model, although it does not tell the whole story of how atoms are structured, is useful in understanding the relationship between electron behaviour and energy interactions within the atom. In fact, it is with knowledge of these energy levels that Becquerel's unknowing discovery of thermionic electron emission can be explained.

Thermionic electron emission theory

How then, does this Rutherford-Bohr model help to explain thermionic electron emission? Simply put, electron emission happens when an electron's kinetic energy becomes great enough to escape the attractive force of the positively charged nucleus. This can occur in different ways, but in the case of thermionic electron emission, electrons in the atom gain kinetic energy when the atom's temperature is increased. As the atom's temperature increases its electrons gain energy, moving up the energy levels away from the nucleus until a critical point of kinetic energy is reached.

This critical point is known as the metal's 'work function', and is an intrinsic property of a given material. It is defined as the 'minimum amount of energy required to remove an electron from the surface of a material'. Once this work function is reached, electrons progress past the final energy level and electron emission occurs. These electrons are then referred to as free electrons, or thermions.

This phenomenon, though discovered earlier by both Becquerel and Guthrie, was for some time referred to as the Edison effect. Edison, whilst conducting experiments to improve his new incandescent lamp, discovered that current would flow through a vacuum from a heated filament to a cooler metal surface. Years later, this discovery would pave the way for the invention of the cathode ray tube, and in turn the electron gun.

Thermionic electron emission and the electron gun

The electron gun is an electrical component that produces a concentrated beam of electrons. It is based on the principles of thermionic electron emission and is primarily used in the design of cathode ray tubes.

The basic electron gun is comprised of three main parts: a metal filament cathode that emits free electrons when the temperature is increased, a selection of electrodes that focus the resulting stream of electrons (often called a 'Wehnelt cylinder'), and a highly positive anode to accelerate the free electrons to greater speeds.

A positive 'heating voltage' is applied across the hot cathode, while a much larger positive 'acceleration voltage' is applied to the anode. As the anode has a far greater positive voltage than the hot cathode, the negative free electrons will accelerate towards it at greater and greater speeds. It is the difference in voltage (or potential difference) between the cathode and anode that determines the acceleration of the free electrons in the beam.

Interestingly, these devices resided for a long time in nearly every home. The electron gun was absolutely pivotal in the invention of the television. Before the invention of the flat-screen TV, the picture on television screens was created using beams from three electron guns. This is why 'old-fashioned' televisions were much deeper units; they needed enough space to accelerate the free electrons to the screen!

Speeds of electrons in thermionic electron emission

So, how fast exactly do electrons emitted from a metal surface travel? Well, that's easy! The kinetic energy equation can be used to work out the emitted electron's velocity, provided we know the kinetic energy of the electron when it is emitted.

\[E_k = \frac{1}{2} mv^2\]

where: E_k = the kinetic energy of the electron, (J)m = the mass of the electron (kg)v = the velocity of the electron (ms^-1)

The acceleration of free electrons through a potential difference

Electrons are incredibly tiny particles with tiny masses. Though they move incredibly fast, they have extremely small kinetic energies. For this reason, a whole new unit of energy was created just for them: the electron-volt (eV). To understand what an electron-volt is, it is important to understand what happens to a free electron travelling through a potential difference between two points.

We've already seen how a potential difference was used to accelerate free electrons in the electron gun; the negative electrons just accelerate toward the more positive electrode (cathode). How much these free electrons accelerate, and in turn how much kinetic energy they gain, is dependent on the potential difference they travel through. The greater the potential difference, the more kinetic energy the electron will have gained.

\[E_k = eV\]

where: E_k = kinetic energy (J)e = the charge of an electron (C)V= the potential difference (voltage) the electron is accelerated through (V)

Here, e is the charge of an electron, and V is the potential difference that the electron has been accelerated through. An electron-volt therefore, is the energy gained by a free electron accelerated through a 1-volt potential difference, or:

When combined with the equation for kinetic energy, it is possible to find the velocity gained by this free electron from the potential difference.

\[eV = \frac{1}{2} mv^2\]