The Franck-Hertz Experiment

What the Apparatus Actually Does

The Franck-Hertz tube contains a small amount of mercury heated to produce a low-pressure vapor, along with three electrodes: a heated cathode that emits electrons, a wire mesh grid held at a variable accelerating voltage, and a collector plate held at a slightly lower voltage than the grid, creating a small retarding field. Electrons boil off the hot cathode with almost no kinetic energy and are pulled toward the grid by the accelerating voltage, gaining speed as they cross the gap. Along the way they inevitably collide with mercury atoms drifting through the same space.At low accelerating voltages, these collisions are elastic. Because an electron is thousands of times lighter than a mercury atom, an elastic collision barely slows it down, much like a ping-pong ball bouncing off a bowling ball. The electron sails through the grid, crosses the small retarding gap, and reaches the collector, registering as current on a sensitive meter. As the accelerating voltage rises, more electrons arrive with more energy, and the current rises smoothly, exactly as classical physics would predict for a simple vacuum tube.The surprise appears once the accelerating voltage approaches roughly 4.9 volts. At that point, electrons reach the region near the grid with just enough kinetic energy to excite a mercury atom's outermost electron from its ground state to its first excited state in a single inelastic collision. The incident electron gives up essentially all of its kinetic energy in that instant, and having lost its energy so close to the grid, it can no longer climb the retarding voltage between grid and collector. The current drops sharply. Push the voltage a little higher and the electrons that collide early in the tube still have enough leftover energy to reach the grid, so the current climbs again, until the next threshold is crossed and a second wave of electrons loses its energy partway through, producing a second dip. This simulator reproduces that entire chain of cause and effect, from electron acceleration to inelastic collision to current collection, so you can watch each stage unfold rather than just read about it.

Why the Dips Are Evenly Spaced

The single most telling feature of the Franck-Hertz curve is that the dips repeat at almost perfectly regular intervals, roughly every 4.9 volts for mercury vapor. This regularity is not a coincidence of the apparatus, it is a direct consequence of the fact that mercury atoms can only accept energy in one fixed amount when excited from the ground state to the first excited state, no more and no less.Consider what happens as the accelerating voltage is pushed well beyond the first dip. An electron leaving the cathode now has enough distance and voltage available to gain 4.9 electron-volts of energy, lose it all in a collision near the start of the tube, and then reaccelerate through the remaining distance, gaining another 4.9 electron-volts before reaching the grid region a second time. If it collides inelastically again, it loses that second packet of energy too, and once more arrives at the collector without enough energy to overcome the retarding field. This produces a second dip at roughly twice the voltage of the first, then a third dip near three times that voltage, and so on. Each dip corresponds to one additional inelastic collision fitting into the electron's journey down the tube.If atomic energy absorption were continuous, as classical physics assumed before quantum theory, electrons could lose any small fraction of their energy in a collision, and the current would simply rise smoothly with voltage, with no dips at all. The fact that the dips are sharp, repeating, and spaced by a constant voltage interval demonstrates that mercury atoms accept energy only in a single discrete packet corresponding to the gap between two specific energy levels. The size of that voltage interval is not arbitrary either, it corresponds almost exactly to the energy of the ultraviolet spectral line mercury emits when the excited atoms relax back to the ground state, tying the collision experiment directly to atomic spectroscopy. In the simulator, you can trace how the spacing between dips stays essentially constant as you scan the voltage, and see how each successive dip reflects one more full absorption cycle happening somewhere along the tube.

Connecting the Dips to Bohr's Model

When Niels Bohr proposed his model of the atom in 1913, he made a radical claim, electrons in an atom cannot occupy just any energy, they are restricted to a discrete set of allowed orbits, each with a specific, fixed energy. An atom could absorb or emit energy only by jumping an electron between these allowed levels, and the amount of energy involved in each jump had to exactly match the difference between two levels. At the time, the strongest evidence for this idea came from atomic spectra, the sharp, discrete lines of light emitted by excited gases, which Bohr's model explained beautifully for hydrogen.What the Franck-Hertz experiment added was a completely independent line of evidence, obtained not from light but from particle collisions. Franck and Hertz showed that free electrons, colliding with atoms in a gas, could only transfer energy to those atoms in specific fixed quantities, never a continuous range of smaller amounts. That is exactly what Bohr's model predicted, an atom's ground state and first excited state are separated by a fixed energy gap, and nothing in between is allowed. An electron with less than 4.9 electron-volts of kinetic energy simply cannot excite the atom at all and can only bounce off elastically. An electron with exactly 4.9 electron-volts, or a small multiple of it, can transfer that energy in one clean, sudden event.This convergence of two very different kinds of measurement, optical spectroscopy and electron scattering, both pointing to the same discrete energy gap, gave physicists confidence that quantization was a real, physical feature of atoms rather than a mathematical trick invented to fit spectral lines. Franck and Hertz initially interpreted their results in terms of ionization energy rather than excitation energy, and it took further analysis, partly by Bohr himself, to correctly connect the 4.9 volt spacing to the excitation of mercury's first excited state. Once that connection was made, the experiment became one of the clearest, most direct demonstrations available that atoms truly do possess quantized internal energy levels, observable using nothing more exotic than a heated tube, some mercury vapor, and a battery.

The 1925 Nobel Prize and Its Legacy

James Franck and Gustav Hertz were awarded the Nobel Prize in Physics in 1925, eleven years after their original experiment, for the discovery of the laws governing the impact of an electron upon an atom. The delay reflected how long it took the broader physics community, and to some extent Franck and Hertz themselves, to fully appreciate that their tabletop measurement of current dips was a direct confirmation of Bohr's quantized atom, one of the pillars on which the emerging edifice of quantum mechanics would be built.The experiment's influence extended well beyond its original result. It established electron impact spectroscopy as a legitimate technique for probing atomic and molecular energy levels, a method still used today to study excitation energies in gases the optical spectra of which are difficult to interpret. It also became, and remains, one of the most widely repeated experiments in university physics laboratories worldwide, precisely because the equipment is relatively simple, the physics is unambiguous, and the result, a series of clean, regularly spaced dips, is immediately visible and strikingly convincing to a student encountering quantum ideas for the first time.Historically, the Franck-Hertz experiment sits alongside the photoelectric effect and the discrete spectral lines of hydrogen as one of the handful of experimental results from the early twentieth century that could not be reconciled with classical physics and demanded a fundamentally new framework. Where the photoelectric effect showed that light itself carries energy in discrete quanta, Franck and Hertz showed that matter, specifically the internal structure of atoms, also stores and exchanges energy only in discrete amounts. Together these results helped convince a skeptical scientific community that the strange rules of quantum theory were not a mathematical convenience but a genuine description of how nature behaves at the atomic scale, a legacy this simulator lets you rediscover firsthand by running the experiment yourself.

Reading the Current-Voltage Curve in the Simulator

When you run the simulation, the accelerating voltage is the control you sweep, and the current reaching the collector is the quantity you watch. At very low voltage, the current is essentially zero because electrons leave the cathode too slowly to overcome the small retarding field near the collector. As voltage increases, current rises roughly following the pattern expected for a simple space-charge-limited tube, until the first threshold near 4.9 volts is reached, where inelastic collisions begin removing electrons from the collected current and the curve turns sharply downward.Beyond that first dip, watch how the current recovers and climbs again as voltage increases further, only to dip a second time near twice the threshold voltage, then a third time near three times the threshold, and so on for as many dips as the tube geometry and voltage range allow. Pay attention to the spacing between successive dips rather than their exact position, that constant spacing is the real physical signature of quantization, and it should remain essentially the same from one dip to the next across the whole sweep.The simulator also lets you explore how the picture changes if you adjust vapor density, tube length, or gas identity. A longer tube or a denser vapor increases the chance an electron undergoes an inelastic collision before reaching the grid, which sharpens and deepens the dips. Switching from mercury to neon changes the threshold voltage entirely, since neon's first excited state sits at a different energy above its ground state, illustrating that the specific dip spacing is a property of the particular atom being studied, not a universal constant. By manipulating these parameters directly, you gain an intuitive, hands-on sense of how a single atomic property, the energy gap between two quantum states, manifests as a macroscopic, measurable pattern in an electrical current, precisely the leap of reasoning that made this experiment so persuasive a century ago.

Frequently asked questions

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Everything above runs in your browser — open The Franck-Hertz Experiment and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.