12. The Franck-Hertz Experiment

Introduction

One of the earliest experiments to confirm the quantum nature of the energy levels of the atom was the 1914 experiment performed by Franck and Hertz.  The classical picture of the atom has electrons moving in orbits about the nucleus much like the planets move about the Sun.  The size of the orbit of an electron is related to the energy of the electron so that large radius electron orbits have more energy than small radius orbits.  (The nuclei contain protons and neutrons and are very massive in comparison  to the electrons.) The classical picture of the atom allows "bound" electron orbits of every size and energy.  However, the (old) quantum theory allows the "bound" electrons to have orbits only of select radius (or energy); all the other orbits are not allowed except when an "bound" electron makes as transition from one allowed orbit to another.

Atoms can absorb energy in several ways.  In the Franck-Hertz experiment, "free" electrons are accelerated to give them energy before colliding (or "interacting") with the electrons "bound" to the atoms.   (A collision of the free electron with a nuclei does NOT change the energy of the free electron because this collision is energy conserving or "elastic".)  If the energy (or speed) of the "free" electron is small, the atom's energy after the collision is the same as before the collision since there is not enough energy to raise a "bound" electron to a higher energy orbit.  However, if the free electron's energy is large enough, then the free electron can provided enough energy to raise an electron bound to the atom to a higher energy orbit.  In this process, the free electron looses energy to the atom and an electron bound to the atom is left in a higher energy orbit as a result of the interaction.    After a short time, the higher energy electron of the atom looses part of its energy in the form (of a quantum) of light or photon (this can be observed with a spectrometer) and the electron drops to the  smallest allowed orbit.  This is the basic Franck-Hertz experiment.

The Franck-Hertz apparatus has a glass tube containing neon which effectively has 20 ev (or electron volts) of energy between the lowest energy state and the next higher one.  (An electron volt is the energy acquired by an electron in moving through a potential of one volt;  1  ev = 1.6×(10^(-10)) Joules.)  The "free electrons" are obtained from a heated filament (called a "heater") much like the filament of a light bulb in your home.  The "free electrons" are accelerated by the potential between the heater (or cathode because it has a negative potential) and the grid.  (A grid is physically much like a metal screen on a door or window and it allows most of the electrons to pass through.)  Finally, the electrons are attracted to the plate which is kept at a small negative potential relative the grid so that a current does not flow unless the electrons have enough energy to reach the plate.  A sketch of the Franck-Hertz tube is indicated below:

The accelerating voltage is increased in increments of about 0.1 volts starting with (Subscript[V, A])=0 volts and ending at about (Subscript[V, A])=60 - 70 volts.  The plate current read by measuring the voltage drop (Subscript[V, P]) across the plate resistor.  A sketch of a graph of the data is indicated below:

Theory

The free electrons collide elastically until they have an energy of about 20 ev. (Actually the voltage is more like 18.5 volts since there is a 1.5 volt "contact potential" between the plate and cathode.) The plate current increases gradually since more free electrons have enough energy to reach the plate.  At about 20 volts, the free electrons have enough energy to raise the electrons attached to the neon  atoms to a higher energy level.  At about this energy, the neon gas begins to "glow" in a layer between the cathode and grid since it is in this layer where the neon atoms are "excited" or raised to the 1st energy state above the ground state.  (Actually the atomic energy structure is quick complicated and there are cluster of energy levels at about 20 ev above the ground state.) The free electrons now loose energy to the atomic electrons and most of the free electrons can no longer reach the plate.  This accounts for the drop in the plate current.

As the voltage is increased above 20 volts, more plate current flows again until a second peak is reached at about 40 volts.  The plate current then drops off quickly again to a valley.  This valley is interpreted as the free electrons exciting a second "layer" of neon atoms to the first energy state above the ground state.  The "glow" in the neon is due to the neon atoms going back to the ground state and giving off photons of light.  There is a third peak and valley observable at about 60 ev and so on.

Lab Report

Graph your grid voltage versus plate voltage data and note the location of the three peaks and valleys you observe.  Look up the quantum energy level diagram for neon and confirm there is a cluster of energy levels about 20 ev above the ground state energy.  Discuss why a classical model of the atom cannot explain the Franck-Hertz data.