Department of Physical Electronics
Faculty of Science, Masaryk University, Brno
Physical laboratory 3
Task D The Franck-Hertz experiment
Tasks
1. Observe the influence of the set parameters on the behaviour of the anode current. Choose
the correct parameters.
2. Measure the dependence of the anode current on the accelerating voltage and determine the
energy of the lowest excitation level of the rare gas in the tube.
3. Measure the optical spectrum emitted from the Franck-Hertz experiment tube and determine
the identity of the rare gas.
Figure 1: Gustav Hertz.
The principle of the Franck-Hertz experiment
At the beginning of the twentieth century, the new quantum theory was verified mainly using
atomic spectra. In 1914 Franck and Hertz experimentally showed, even without using optical
spectroscopy, that quantum energy levels of electrons exist and correspond to those determined
by the optical emission spectroscopy. Franck and Hertz were awarded the Nobel prize in physics
in 1925 for this work.
The original Franck-Hertz experiment is based on the collisions of electrons with mercury
atoms. When an atom inelastically collides with an energetic particle, a part of mutual kinetic
energy can be transferred to the atom. An electron in such an atom is excited to a higher energy
level. For the atom to be excited by an impact of another particle, mutual kinetic energy must
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Figure 2: Experimental setup of the original Franck-Hertz experiment.
be higher than the lowest excitation energy of the atom. Only then an inelastic collision can take
place. Some time after the excitation (usually a very short time), the excited electron in the atom
returns to its base state while emitting one or more photons.
Franck and Hertz used an experimental apparatus similar to that shown in figure 2 to bombard
vapours of different gasses with electrons of variable energy. The electrons are emitted by a hot
cathode, and they are electrically accelerated towards a grid. A small potential difference is kept
between the grid and a collecting electrode (collector) to decelerate electrons after passing the
grid. The collector current rises with the increasing accelerating voltage only in a specific region.
A steep decrease in the collector current is observed after exceeding a particular value of the
Figure 3: The dependence of the collector current on the accelerating voltage for mercury.
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accelerating voltage. Inelastic collisions occur near the grid as electrons gain the energy of the
lowest excitation level of the studied gas at that region by the accelerating field. The electrons
lose their energy after undergoing the inelastic collision, and they are unable to overcome the
potential difference between the grid and the collector. In such a case, the electron does not
reach the collector, but it lands on the grid instead. Consequently, the collector current steeply
decreases.
An example of such measurement for mercury vapour is shown in figure 3. It was seen that
the dependence of the collector current on the accelerating voltage shows several drops repeated
after approximately 4.9 V. Inelastic collisions occurred near the grid at the accelerating voltage
of 4.9 V, at which the electrons reached the lowest excitation energy of mercury. The collector
current sharply decreased. Each electron could undergo two such consecutive collisions at the
accelerating voltage of 9.8 V. The first one happened approximately halfway between the cathode
and the grid and the second one near the grid itself. Both collisions resulted in the excitation of
mercury to the lowest excitation level. Therefore it is evident that the Franck-Hertz experiment
allows for the measurement of only the lowest excitation energy level of an atom. Nevertheless,
it was the first experiment proving the existence of discrete atomic levels without using optical
spectroscopy, and therefore it was significant for quantum physics.
Experimental setup
Figure 4 shows the experimental setup of the Franck-Hertz experiment we will use in the laboratory.
A hot cathode C, two grids G1 and G2 separated by the distance L and anode A are placed
inside a vacuum tube. The small voltage U1 between the cathode C and the first grid G1 serves
for the stabilisation of the experiment. The accelerating voltage U2 between the grids G1 and
G2 is used to set the kinetic energy of the electrons. The electrons are then decelerated by the
voltage U3 between the grid G2 and the anode A. If the electron undergoes an inelastic collision
Figure 4: Experimental setup of the Franck-Hertz experiment in the laboratory.
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Figure 5: Measurement apparatus: 1 - Power source, 2 - Vacuum tube, 3 - Voltmeters, 4 - Avantes
spectrometer.
near the second grid G2, the decelerating voltage U3 can cause the electron to land on the grid
G2 rather than on the anode A. The tube is filled with a rare gas. Voltages U1 and U3 can be set
to constant values, voltage U2 can be set to a constant value or generated in a saw-shape.
Experimental procedure
• Work in the regime where U2 is generated in the saw-shape and study the effect of voltages
U1 and U3 on the general shape of the measured anode current. At first set different values of
U3 (keep U1 constant) and observe the I=f(U2) dependence. Do not note the specific data.
Rather make conclusions from your observations and support them based on the physics
applied in the experiment. Repeat the same for constant U3 and different U1.
• Choose at least one suitable combination of U1 and U3. Measure the I=f(U2) dependence
for chosen combination of U1 and U3.
• Determine the energy of the lowest excitation level of the rare gas in the tube. Familiarise
yourselves with the lowest excitation energy levels of rare gases before the laboratory. These
can be found, e.g. on the pages of the National Institute of Standards and Technology
in the Atomic spectra database subsection (http://www.physics.nist.gov/PhysRefData/
contents.html). Compare your results with the tabulated data and identify the present
gas. You can find the spectroscopic notation using roman numerals. Numeral I denotes a
neutral atom, numeral II denotes a singly ionised atom, numeral III a doubly ionised atom
etc. For example, neutral helium atoms are denoted He I.
• Finally, measure the optical spectra of the gas by the available spectrometer. Verify your
gas identification based on the spectral line database (e.g. from the National Institute of
Standards and Technology). You can do this by comparing the positions of the measured
intensive spectral lines with the tabulated positions.