Franck-Hertz experiment

The Franck-Hertz experiment was a physics experiment that provided support for the Bohr model of the atom, a precursor to quantum mechanics. In 1914, the German physicists James Franck and Gustav Ludwig Hertz sought to experimentally probe the energy levels of the atom. The now-famous Franck-Hertz experiment elegantly supported Niels Bohr's model of the atom, with electrons orbiting the nucleus with specific, discrete energies. Franck and Hertz were awarded the Nobel Prize in Physics in 1925 for this work.

The Franck-Hertz experiment confirmed Bohr's quantized model of the atom by demonstrating that atoms could indeed only absorb (and be excited by) specific amounts of energy (quanta).

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The experiment

  The classic experiment involved a tube containing low pressure gas fitted with three electrodes: an electron emitting cathode, a mesh grid for acceleration, and an anode. The anode was held at a slightly negative electrical potential relative to the grid (although positive compared to the cathode), so that electrons had to have a small amount of kinetic energy to reach it after passing the grid. Instruments were fitted to measure the current passing between the electrodes, and to adjust the potential difference (voltage) between the cathode (negative electrode) and the accelerating grid.

• At low potential differences—up to 4.9 volts when the tube contained mercury vapour—the current through the tube increased steadily with increasing potential difference. The higher voltage increased the electric field in the tube and electrons were drawn more forcefully towards and through the accelerating grid.
• At 4.9 volts the current drops sharply, almost back to zero.
• The current increases steadily once again if 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.
• This series of dips in current at approximately 4.9 volt increments will visibly continue to potentials of at least 100 volts.

Interpretation of results

Franck and Hertz were able to explain their experiment in terms of elastic and inelastic collisions. At low potentials, the accelerated electrons acquired only a modest amount of kinetic energy. When they encountered mercury atoms in the tube, they participated in purely elastic collisions. This is due to the prediction of quantum mechanics that an atom can absorb no energy until the collision energy exceeds that required to lift an electron that is bound to the atom into a higher energy state.

With purely elastic collisions, the total amount of kinetic energy in the system remains the same. Since electrons are over one thousand times less massive than even the lightest atoms, this meant that the electrons held on to the vast majority of that kinetic energy. Higher potentials served to drive more electrons through the grid to the anode and increase the observed current, until the accelerating potential reached 4.9 volts.

The lowest energy electronic excitation a mercury atom can participate in requires 4.9 electron volts (eV). When the accelerating potential reached 4.9 volts, each free electron possessed exactly 4.9 eV of kinetic energy (above its rest energy at that temperature) when it reached the grid. Consequently, a collision between a mercury atom and a free electron at that point could be inelastic: that is, a free electron's kinetic energy could be converted into potential energy by raising the energy level of an electron bound to a mercury atom: this is called exciting the mercury atom. With the loss of all its acquired kinetic energy in this way, the free electron can no longer overcome the slight negative potential at the ground electrode, and the measured current drops sharply.

As the voltage is increased, electrons will participate in one inelastic collision, lose their 4.9 eV, but then continue to be accelerated. In this manner, the current rises again after the accelerating potential exceeds 4.9 V. At 9.8 V, the situation changes again. There, each electron now has just enough energy to participate in two inelastic collisions, excite two mercury atoms, and then be left with no kinetic energy. Once again, the observed current drops. At intervals of 4.9 volts this process will repeat; each time the electrons will undergo one additional inelastic collision.

Effect in other gases

A similar pattern is observed with neon gas, but at intervals of approximately 19 volts. The process is identical, just with a much different threshold. One additional difference is that a glow will appear near the accelerating grid at 19 volts--one of the transitions of relaxing neon atoms emits red-orange light. This glow will move closer to the cathode with increasing accelerating potential, to whatever point in the tube the electrons acquire the 19 eV required to excite a neon atom. At 38 volts two distinct glows will be visible: one between the cathode and grid, and one right at the accelerating grid. Higher potentials, spaced at 19 volt intervals, will result in additional glowing regions in the tube.

References

• An Interactive Simulation of The Franck-Hertz Experiment
• The Franck-Hertz Experiment at Hyperphysics
• Up-to-date literature on the Franck-Hertz Experiment
• J. Franck and G. Hertz (1914). "Über Zusammenstöße zwischen Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben". Verh. Dtsch. Phys. Ges. 16: 457–467.
• G. Rapior, K. Senstock, and V. Baev (2006). "New features of the Franck-Hertz experiment". Amer. J. Phys. 74: 423–428.