Franck Hertz experiment was first studied in the year 1914 by James Franck and Gustav Hertz and presented to the German Physical Society. It was the first electrical measurement to show the quantum nature of atoms. A vacuum tube was designed to study the energetic electrons that flew through a thin vapour of mercury atoms. It was discovered that only a specific amount of atom’s kinetic energy would lose as the electrons collide with the mercury atom.

## Franck Hertz Experiment

### Aim:

To demonstrate the concept of quantization of the energy levels according to the Bohr’s model of an atom.

### Materials Required:

Following are the list of materials required for this experiment:

- Mercury filled Franck-Hertz tube
- Neon filled Franck-Hertz tube
- Oven
- A control unit for power supply
- A DC amplifier

### Theory:

The original experiment used a heated vacuum tube of temperature 115 °C with a drop of mercury of vapor pressure 100 Pa. the tube is fitted with three electrodes, they are an electron emitting hot cathode, a metal mesh grid, and an anode. To draw the emitted electrons, the gird’s voltage is positive with respect to the cathode. The electric current measured in the experiment is the result of the movement of electrons from the grid to the anode. The electric potential of an anode is slightly negative than the grid so that the electrons have the kinetic energy the same as in the grid. The experiment was explained in terms of elastic and inelastic collisions between the electrons and the mercury atoms.

The graphs show the dependence of the electric current flowing out of the anode and the electric potential between the grid and the cathode. Following are the observations from the graph:

- With the steady increase in the potential difference, the current increases steadily through the tube.
- The current drops almost to zero at 4.9 volts.
- Again there is an increase in the current as voltage increases to 9.8 volts is reached.
- Again a similar drop is observed at 9.8 volts.

## What Is An Elastic Collision?

An elastic collision is defined as an encounter between two bodies such that the total kinetic energy of the two bodies remains the same. During the collision, kinetic energy is first converted to potential energy which is related to repulsive force between the particles which is converted back to kinetic energy. Rutherford back-scattering is an example of an elastic collision.

- One-dimensional form of elastic collision of particles 1 and 2:

\(\frac{1}{2}m_{1}u_{1}^{2}+\frac{1}{2}m_{2}u_{2}^{2}=\frac{1}{2}m_{1}v_{1}^{2}+\frac{1}{2}m_{2}v_{2}^{2}\) |

Where,

- m
_{1}, m_{2}are the masses of particles 1 and 2 - u
_{1}, u_{2}are the velocities of particles before collision - v
_{1}, v_{2}are the velocities of particles after collision - The magnitudes of the velocities of the particles after the collision is given with two-dimensional form:

\({v}’_{1}=v_{1}\frac{\sqrt{m_{1}^{2}+m_{2}^{2}+2m_{1}m_{2}cos\Theta }}{m_{1}m_{2}}\) |

\({v}’_{2}=v_{1}\frac{2m_{1}}{m_{1}+m_{2}}sin\frac{\Theta }{2}\) |

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## What Is An Inelastic Collision?

An inelastic collision is defined for the two bodies whose kinetic energies are not conserved due to internal friction. Macroscopic collisions result in effects, vibrations of the atoms and the deformation of the bodies. Following is the formula of one-dimensional collision for particles a and b:

\(v_{a}=\frac{C_{R}m_{b}(u_{b}-u_{a})+m_{a}u_{a}+m_{b}u_{b}}{m_{a}+m_{b}}\) |

\(v_{b}=\frac{C_{R}m_{a}(u_{a}-u_{b})+m_{a}u_{a}+m_{b}u_{b}}{m_{a}+m_{b}}\) |

Where,

- v
_{a}is the final velocity of the first object after impact - v
_{b}is the final velocity of the second object after impact - u
_{a}is the initial velocity of the first object before impact - u
_{b}is the initial velocity of the second object before impact - m
_{a}is the mass of the first object - m
_{b}is the mass of the second object - C
_{R}is the coefficient of restitution (ratio of final and initial relative velocities)