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Franck–Hertz Experiment
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The Franck–Hertz Experiment was the first electrical measurement to clearly show the
quantum nature of atoms, and thus "transformed our understanding of the world". It was
presented on April 24, 1914 to the German Physical Society in a paper by James Franck and
Gustav Hertz. Franck and Hertz had designed a vacuum tube for studying energetic electrons
that flew through a thin vapor of mercury atoms. They discovered that, when an electron
collided with a mercury atom, it could lose only a specific quantity (4.9 electron volts) of its
kinetic energy before flying away. This energy loss corresponds to decelerating the electron
from a speed of about 1.3 million meters per second to zero. A faster electron does not
decelerate completely after a collision, but loses precisely the same amount of its kinetic
energy. Slower electrons merely bounce off mercury atoms without losing any significant
speed or kinetic energy.
These experimental results proved to be consistent with the Bohr model for atoms that had
been proposed the previous year by Niels Bohr. The Bohr model was a precursor of quantum
mechanics and of the electron shell model of atoms. Its key feature was that an electron
inside an atom occupies one of the atom's "quantum energy levels". Before a collision, an
electron inside the mercury atom occupies its lowest available energy level. After the
collision, the electron inside occupies a higher energy level with 4.9 electron volts (eV) more
energy. This means that the electron is more loosely bound to the mercury atom. There were
no intermediate levels or possibilities in Bohr's quantum model. This feature was
"revolutionary" because it was inconsistent with the expectation that an electron could be
bound to an atom's nucleus by any amount of energy. A planet can be bound to a star by any
energy.
In a second paper presented in May 1914, Franck and Hertz reported on the light emission by
the mercury atoms that had absorbed energy from collisions. They showed that the
wavelength of this ultraviolet light corresponded exactly to the 4.9 eV of energy that the
flying electron had lost; for visible light, different wavelengths correspond to different colors.
The relationship of energy and wavelength had also been predicted by Bohr. After a
presentation of these results by Franck a few years later, Albert Einstein is said to have
remarked, "It's so lovely it makes you cry."
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On December 10, 1926, Franck and Hertz were awarded the 1925 Nobel Prize in Physics "for
their discovery of the laws governing the impact of an electron upon an atom."
The experiment
Franck and Hertz's original experiment used a heated vacuum tube containing a drop of
mercury; they reported a tube temperature of 115 °C, at which the vapor pressure of mercury
is about 100 pascals (and far below atmospheric pressure). A contemporary Franck–Hertz
tube is shown in the photograph. It is fitted with three electrodes: an electron-emitting, hot
cathode; a metal mesh grid; and an anode. The grid's voltage is positive relative to the
cathode, so that electrons emitted from the hot cathode are drawn to it. The electric current
measured in the experiment is due to electrons that pass through the grid and reach the anode.
The anode's electric potential is slightly negative relative to the grid, so that electrons that
reach the anode have at least a corresponding amount of kinetic energy after passing the grid.
The graphs published by Franck and Hertz (see figure) show the dependence of the electric
current flowing out of the anode upon the electric potential between the grid and the cathode.
At low potential differences — up to 4.9 volts — the current through the tube increased
steadily with increasing potential difference. This behavior is typical of true vacuum tubes
that don't contain mercury vapor; larger voltages lead to larger "space-charge limited
current".
At 4.9 volts the current drops sharply, almost back to zero.
The current then increases steadily once again as the voltage is increased further, until 9.8
volts is reached (exactly 4.9+4.9 volts).
At 9.8 volts a similar sharp drop is observed.
While it isn't evident in the original measurements of the figure, this series of dips in current
at approximately 4.9 volt increments continues to potentials of at least 70 volts.
Franck and Hertz noted in their first paper that the 4.9 eV characteristic energy of their
experiment corresponded well to one of the wavelengths of light emitted by mercury atoms in
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gas discharges. They were using a quantum relationship between the energy of excitation and
the corresponding wavelength of light, which they broadly attributed to Johannes Stark and to
Arnold Sommerfeld; it predicts that 4.9 eV corresponds to light with a 254 nm wavelength.
The same relationship was also incorporated in Einstein's 1905 photon theory of the
photoelectric effect. In a second paper, Franck and Hertz reported the optical emission from
their tubes, which emitted light with a single prominent wavelength 254 nm. The figure at the
right shows the spectrum of a Franck–Hertz tube; nearly all of the light emitted has a single
wavelength. For reference, the figure also shows the spectrum for a mercury gas discharge
light, which emits light at several wavelengths besides 254 nm. The figure is based on the
original spectra published by Franck and Hertz in 1914. The fact that the Franck–Hertz tube
emitted just the single wavelength, corresponding nearly exactly to the voltage period they
had measured, was very important.
The Franck–Hertz experiment and early quantum theory
While Franck and Hertz were unaware of it when they published their experiments in 1914,
in 1913 Niels Bohr had published a model for atoms that was very successful in accounting
for the optical properties of atomic hydrogen. These were usually observed in gas discharges,
which emitted light at a series of wavelengths. Ordinary light sources like incandescent light
bulbs emit light at all wavelengths. Bohr had calculated the wavelengths emitted by hydrogen
very accurately.
The fundamental assumption of the Bohr model concerns the possible binding energies of an
electron to the nucleus of an atom. The atom can be ionized if a collision with another
particle supplies at least this binding energy. This frees the electron from the atom, and leaves
a positively charged ion behind. There is an analogy with satellites orbiting the earth. Every
satellite has its own orbit, and practically any orbital distance, and any satellite binding
energy, is possible. Since an electron is attracted to the positive charge of the atomic nucleus
by a similar force, so-called "classical" calculations suggest that any binding energy should
also be possible for electrons. However, Bohr assumed that only a specific series of binding
energies occur, which correspond to the "quantum energy levels" for the electron. An electron
is normally found in the lowest energy level, with the largest binding energy. Additional
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levels lie higher, with smaller binding energies. Intermediate binding energies lying between
these levels are not permitted. This was a revolutionary assumption.
Franck and Hertz had proposed that the 4.9 V characteristic of their experiments was due to
ionization of mercury atoms by collisions with the flying electrons emitted at the cathode. In
1915 Bohr published a paper noting that the measurements of Franck and Hertz were more
consistent with the assumption of quantum levels in his own model for atoms. In the Bohr
model, the collision excited an internal electron within the atom from its lowest level to the
first quantum level above it. The Bohr model also predicted that light would be emitted as the
internal electron returned from its excited quantum level to the lowest one; its wavelength
corresponded to the energy difference of the atom's internal levels, which has been called the
Bohr relation. Franck and Hertz's observation of emission from their tube at 254 nm was also
consistent with Bohr's perspective. Writing following the end of World War I in 1918, Franck
and Hertz had largely adopted the Bohr perspective for interpreting their experiment, which
has become one of the experimental pillars of quantum mechanics. As Abraham Pais
described it, "Now the beauty of Franck and Hertz's work lies not only in the measurement of
the energy loss E2-E1 of the impinging electron, but they also observed that, when the energy
of that electron exceeds 4.9 eV, mercury begins to emit ultraviolet light of a definite
frequency ν as defined in the above formula. Thereby they gave (unwittingly at first) the first
direct experimental proof of the Bohr relation!" Franck himself emphasized the importance of
the ultraviolet emission experiment in an epilogue to the 1960 Physical Science Study
Committee (PSSC) film about the Franck–Hertz experiment.
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