User's Manual
Franck-Hertz Experiment Introduction
5
012-14264A
Introduction
In 1914, James Franck and Gustav Hertz discovered in the course of their investigations an “energy loss in distinct steps
for electrons passing through mercury vapor”, and a corresponding emission at the ultraviolet line (= 254 nm) of mer-
cury. As it is not possible to observe the light emission directly, demonstrating this phenomenon requires extensive and
cumbersome experiment apparatus. They performed this experiment that has become one of the classic demonstrations
of the quantization of atomic energy levels. They were awarded the Nobel Prize for this work in 1925.
In this experiment, we will repeat Franck and Hertz's energy-loss observations, using argon, and try to interpret the data
in the context of modern atomic physics. We will not attempt the spectroscopic measurements, since the emissions are
weak and in the extreme ultraviolet portion of the spectrum.
Principle of the Experiment
The Franck-Hertz tube is an evacuated glass cylinder with four electrodes (a “tetrode”) which
contains argon. The four electrodes are: an indirectly heated oxide-coated cathode as an electron
source, two grids G
1
and G
2
and a plate A which serves as an electron collector (anode A). Grid
1 (G
1
) is positive with respect to the cathode (K) (about 1.5 V). A variable potential difference is
applied between the cathode and Grid 2 (G
2
) so that electrons emitted from the cathode can be
accelerated to a range of electron energies. The distance between the cathode and the anode is
large compared with the mean free path length in the argon in order to ensure a high collision
probability. On the other hand, the separation between G
2
and the collector electrode (A) is
small. A small constant negative potential U
G2A
(“retarding potential”) is applied between G
2
and the collector plate A (i.e. A is less positive than G
2
). The resulting electric field between G
2
and collector electrode A opposes the motion of electrons to the collector electrode, so that elec-
trons which have kinetic energy less than e•U
G2A
at Grid 2 cannot reach the collector plate A.
As will be shown later, this retarding voltage helps to differentiate the electrons having inelastic
collisions from those that don’t.
A sensitive current amplifier is connected to the collector electrode so that the current due to the
electrons reaching the collector plate may be measured. As the accelerating voltage is increased,
the following is expected to happen: Up to a certain voltage, say V
1
, the plate current I
A
will
increase as more electrons reach the plate. When the voltage V is reached, it is noted that the plate current, I
A
, takes a
sudden drop. This is due to the fact that the electrons just in front of the grid G
2
have gained enough energy to collide
inelastically with the argon atoms. Having lost energy to the argon atom, they do not have sufficient energy to over-
come the retarding voltage between G
2
and collector electrode A. This causes a decrease in the plate current I
A
. Now as
the voltage is again increased, the electrons obtain the energy necessary for inelastic collisions before they reach the
anode. After the collision, by the time they reach the grid, they have obtained enough energy to overcome the retarding
voltage and will reach the collector plate. Thus I
A
will increase. Again when a certain voltage V
2
is reached we note
that I
A
drops. This means that the electrons have obtained enough energy to have two inelastic collisions before reach-
ing the grid G
2
, but have not had enough remaining energy to overcome the retarding voltage. Increasing the voltage
again, I
A
starts upward until a third value, V
3
, of the voltage is reached when I
A
drops. This corresponds to the elec-
trons having three inelastic collisions before reaching the anode, and so on. The interesting fact is that V
3
- V
2
equals
V
2
- V
1
, etc., which shows that the argon atom has definite excitation levels and will absorb energy only in quantized
amounts.