Franck–Hertz Experiment

One-Sentence Significance

The Franck–Hertz experiment showed that atoms absorb energy from electron collisions in discrete excitation steps.

What Was Measured

Electrons are accelerated through a gas, historically mercury vapor, and the collected current is measured as a function of accelerating voltage. The current shows repeated drops when electrons acquire enough kinetic energy to excite the atoms in inelastic collisions.

For mercury, the first prominent excitation energy is about

$$4.9\,\mathrm{eV}.$$

After an inelastic collision, an electron loses roughly this energy and is less able to reach the collecting electrode.

What It Showed

The atoms did not absorb arbitrary small amounts of collision energy. They had discrete excitation energies. This supported the same quantized-level picture suggested by atomic spectra, but using electron-impact energy loss rather than emitted wavelengths alone.

The experiment gave especially direct evidence that atomic internal energies are quantized.

What It Did Not Show By Itself

The experiment did not by itself derive the Schrödinger equation or reveal the full atomic wavefunction. It also did not show that every collision is inelastic once the threshold is crossed; it showed threshold structure in aggregate current.

Real Franck–Hertz tubes involve contact potentials, gas pressure, electron energy spread, and apparatus geometry. The clean textbook plot is an idealized summary of the threshold physics.

Modern Interpretation

The atom has stationary states with energies $E_n$. An incident electron can transfer energy when

$$K_{\mathrm{electron}} \ge E_n-E_0.$$

The excited atom later decays radiatively or through other channels. The threshold in electron energy and the associated spectral emission are two views of the same discrete energy-level structure.

Canonical Links

• Full Historical Page
• Atomic Spectra
• Energy Eigenstates
• Transition Probabilities
• Spectra

Common Myths

• The current drops because electrons disappear. They mostly lose kinetic energy in inelastic collisions and fail to overcome the retarding field.
• The experiment measured atomic orbits directly. It measured collision thresholds.
• The threshold energy is universal. It depends on the atom and transition.
• A real tube is perfectly monoenergetic. Electron energy spread and contact potentials matter.

Quick Check

Why does a current minimum appear when the accelerating voltage first reaches an excitation threshold?

Solution

At threshold, electrons can lose a fixed amount of kinetic energy by exciting atoms. After this inelastic loss, many electrons no longer have enough energy to reach the collector against the retarding field, so the measured current drops.

References

• J. Franck and G. Hertz, “Ueber Zusammenstoesse zwischen Elektronen und Molekuelen des Quecksilberdampfes und die Ionisierungsspannung desselben,” Verhandlungen der Deutschen Physikalischen Gesellschaft 16, 457-467, 1914.
• J. Franck and G. Hertz, “Ueber die Erregung der Quecksilberresonanzlinie 253.6 nm durch Elektronenstoesse,” Verhandlungen der Deutschen Physikalischen Gesellschaft 16, 512-517, 1914.
• M. Jammer, The Conceptual Development of Quantum Mechanics, 2nd ed., American Institute of Physics, 1989.