Utah State University
From the SelectedWorks of Mario Yuuji Harper
April 17, 2013
Franck-Hertz Experiment
Mario Yuuji Harper, Utah State University
Blake Moore, Utah State University
Available at: http://works.bepress.com/mario_harper/3/
Franck-Hertz Experiment
Mario Harper and Blake Moore
USU Physics
Utah State University, Logan, UT 84332-4414
Introduction
Abstract
The apparatus used for the experiment consist of a tube containing low
pressure gas, fitted with three electrodes: cathode for electron emission, a
mesh grid for the acceleration of electrons and a collecting plate.
The phenomenon investigated in this experiment was whether or not it was possible to excite atoms by
low-energy electron bombardment, and to determine if the energy transferred from the colliding electrons
were always in discrete amounts. This was investigated using thermally excited electrons that were
accelerated across a potential through a homogenous gas of a single element. A slowing potential was
applied at the anode making electrons that transferred their energy via inelastic collisions to lose their
energy before arriving at the detector, this caused drastic decreases in the current observed. These
decreases in current always occurred at the same accelerating potential, which can be interpreted as
electrons only being able to transfer discrete amounts of energy to atoms, and this energy correspondingly
associates with the allowable energy levels within the atoms.
With the help of thermal excitation emission, electrons are boiled off by a
heated cathode and accelerated toward a grid which is held at a positive
potential, relative to the cathode. The collecting plate is at a lower potential
and is held negative with respect to mesh grid. If electrons have sufficient
energy upon reaching the grid, they will pass through and reach the
collecting plate thus causing a measurable current as can be read by an
ammeter. Electrons which do not have sufficient energy on reaching the grid
will be slowed down, and will fall back to the grid. The experimental results
can confirm the existence of discrete energy levels of atoms.
2 Inelastic collision
1 Inelastic collision
Elastic collision
In 1914, James Franck and Gustav Hertz performed an experiment which
demonstrated the existence of discrete excited states in mercury atoms,
helping to confirm the quantum theory which predicted that electrons
occupied only discrete, quantized energy states. Electrons were accelerated
across a potential toward a positively charged grid in a glass envelope filled
with mercury vapor. Past the grid was a collection plate which was held at a
small negative voltage with respect to the grid. The values of accelerating
voltage where the current dropped gave a measure of the energy necessary
to force an electron to an excited state.
Method
As long as the electron collision is elastic, the electrons will not lose energy
on colliding with gas molecules in tube. As the accelerating potential
increases, the current also subsequently increases. The interesting
phenomenon occurs when the accelerating potential reaches a particular
value, (12.13eV for Xenon, 19eV for Neon), each electron that posses that
particular energy causes that the collision becomes inelastic. As a result, the
energy level of an electron bound to the atom is raised. Now the electrons at
this potential loses its energy and fails to reach the collecting plate, we can
see this by observing subsequent current drops.
Fig. 1. Typical results and explanation of the Franck-Hertz experiment for Mercury.
Fig. 2. Full spectrum emission of Neon, both visible and not visible.
Theory
(b)
Fig. 3. Visible spectrum of Xenon
(a)
We can view quantized energy states as a function of wavelength and
energies. For a bounded particle, the wave function is similar to that of a
standing wave. The standing wave (bounded) can only have integer
relations to its state, at other states the waves interfere destructively,
resulting in zero probability density.
(a)
Electrons can be seen as a standing wave in its bounded orbits. If we view
the electron as existing in a potential well, it naturally follows that we
should get a standing wave (and correlating energy and wavelength). This
means that the electron cannot absorb any energy below a certain
threshold, as it cannot exist at that energy. However, at a quantized energy,
the electron can absorb energy and move into a new bounded orbit that is
associated with this new energy state.
The Frank-Hertz experiment supported the theory of the Bohr atom which
was first derived from the study of Hydrogen. The spectral lines of
hydrogen was estimated by the Bohr-Balmer Series, showing a relation
between wavelength and discrete energies as follows:
𝟏
𝟏
𝟏
= 𝑹𝑯 𝟐 − 𝟐
λ
𝟐
𝒏
The Frank-Hertz experiment was designed to test this relation and explained
that all gases have a quantized energy bandwidth that is related to the
spectral lines.
(c)
(b)
(d)
Fig. 6. Diagram of the Franck-Hertz apparatus: a) Heated cathode produces electrons.
b) Positively charged grid accelerates electrons. c) Collecting plate, slightly negative with respect
to the grid so that only those electrons above the threshold will reach it. d) Current from collector
measured as a function of accelerating voltage.
Fig. 3. The wavelength compared to the intensity of the emitted light: a) Neon b) Xenon
References
• R.E. Robson, B. Li, and R.D. White, “Spatially periodic structures in electrons and the Franck-Hertz
experiment,” Journal of Physics B: Molecular and Optical Physics, 33, 3, (2000)
• G.F. Hanne, “What really happens in Franck-Hertz experiment with mercury?,” American Journal of Physics,
56, 8, August (1988)
• Gerald Rapior, Klaus Sengstock, and Valery Baev, “New features of the Franck-Hertz experiment,” American
Journal of Physics, 74, 5, May (2006)
Results
The results we obtain are relatively comparable to the expected results for
both neon and xenon. However, they are not as pronounced as expected.
(a)
Fig. 7. Experimentally acquired data, Current vs. Potential energy: a) Neon b) Xenon
(b)