Franck Hertz Experiment

Aim

The purpose of the experiment is to demonstrate the concept of quantization of the energy levels under Bohr's model of an atom.

Materials required

• Power supply
• A control unit for the power supply
• A DC amplifier
• Oven
• Mercury filled tube
• Neon filled tube

Theory

Originally, the experiment was carried out with the help of a vacuum tube at a temperature of \(115 °C.\) The tube was placed with the help of three electrodes - a cathode which emits electrons, a metal grid and an anode. The voltage of the grid is kept positive with respect to the cathode to draw more electrons towards it.

Since the grid is kept at a positive potential, electrons are accelerated towards it after they are emitted by the cathode. The collecting plate is kept at a negative potential with respect to the grid. Reaching the grid, some will pass through it, and some will be slowed down and fall back into the grid. Those will reach the plate, and the equivalent current will be measured.

As long as the collision is elastic, there is no loss of energy. The current increases as the voltage increase till it reaches a particular value - \(4.9\;\mathrm{eV}\) for Mercury and \(19\;\mathrm{eV}\) for neon, where the collision becomes inelastic. The electron loses its energy and the measured current drops.

Conclusion

This resulted in the prediction of quantum theory that electrons occupy only discrete, quantized energy states.

Applications of the Franck-Hertz experiment

In this section, we will learn more about the two types of collisions, elastic and inelastic, early quantum theory, and the Frank-Hertz experiment with neon gas.

Modeling of Electron Collisions with Atoms

Franck and Hertz explained the experiment in terms of collisions between the electrons and the mercury atoms. When the speed of elastic collision of electrons exceeds about 1.3 million meters per second, it becomes inelastic. This speed is equivalent to the kinetic energy of \(4.9\;\mathrm{eV}\). When the voltage reaches \(4.9\;\mathrm{eV}\), it results in the slowing down of electrons, resulting in a drop in current.

Elastic collision

If the electron does not have enough energy to raise the atom to a higher energy level, the collision of the electron sent onto the atom will be elastic. The electron leaves the gas chamber without losing its energy.

Inelastic collision

If the energy of the electron is higher than the excitation energies of the atom, the atom receives the energy required for its excitation from the electron, and if there is, the electron leaves the gas chamber with its remaining energy. This collision is called an inelastic collision.

Early quantum theory

The basic principle of the Bohr model is that the possible binding energies of an electron to the nucleus of an atom are discrete. A positive ion will be produced as the collision happens at the binding energy, ejecting the electron from the atom.

The Bohr model of the atom, although not a completely up-to-date quantum model of the atom, describes many of the accepted features of atomic theory.

The Bohr model describes the atom as consisting of negatively charged electrons orbiting in circles, due to the Coulomb force, around a central positively charged nucleus. In Bohr's model, the electrons can only orbit at certain radii, and the electron's energy remains constant at each radius. The electron can move from one energy level to another by absorbing or emitting radiation. The Franck-Hertz experiment provided support for the Bohr model of the atom. In the Franck-Hertz experiment, electrons were accelerated through a low-pressure gas.

Hence, the Franck-Hertz experiment is the first direct experimental proof of the Bohr relation.

Graph of Frank Hertz's experiment

Observations from the graph:

• The current through the tube increased gradually with an increasing potential difference at low potential differences up to \(4.9\;\mathrm{V}\). Increased voltages result in a larger space-charge limited current, which is typical of real vacuum tubes that do not contain mercury vapor.
• The current decreases dramatically at \(4.9\;\mathrm{V}\), practically to nothing.
• As the voltage is increased higher, the current increases gradually until it reaches \(9.8\;\mathrm{V}\).
• A similar dramatic decline may be seen at \(9.8\;\mathrm{V}\)
• This series of decreases in current at around\(4.9\;\mathrm{V}\) increments continues until potentials of at least \(70\;\mathrm{V}\), even though it isn't visible in the original measurements of the figure.

Formula of Frank-Hertz experiment

If an electron with an energy of \(4.9\;\mathrm{eV}\) collides with a mercury atom, this gas atom gains energy and becomes unstable. After a short time, it scatters this energy as photons and returns to its ground state. The electron continues on its way with an energy of \(0.04\;\mathrm{eV}\)

An electron with an energy of \(3.85\;\mathrm{eV}\) does not change the energy of the mercury atom. In other words, this electron passes through the atom without excitation.

The largest value of the energy levels is called the ionization energy (\(10.40\;\mathrm{eV}\) for Mercury). If the energy of the electron is greater than or equal to the ionization energy, the atom is ionized. If the mercury atom is excited with an electron with an energy of \(12.00\;\mathrm{eV}\), an electron is removed from the atom and becomes a positively charged ion.