The Franck-Hertz Experiment: Direct Proof That Atoms Have Quantized Energy Levels

Niels Bohr published his model of the hydrogen atom in 1913, proposing that electrons can only occupy specific energy levels and that atoms absorb or emit light in discrete packets when electrons jump between levels. The model fit the hydrogen spectrum beautifully. But fitting a spectrum — matching observed wavelengths to predicted ones — is indirect evidence. What physicists needed was a way to put energy directly into an atom and show that only certain amounts were accepted. In 1914, James Franck and Gustav Hertz did exactly that, using electrons as tiny probes fired through mercury vapor, and the results were definitive.

The Problem That Needed Solving

Bohr's 1913 atom model said that electrons orbit a nucleus at fixed distances, corresponding to fixed energies. An electron in a lower orbit could only jump to a higher one by absorbing exactly the right amount of energy — the difference between the two levels. Nothing less would do.

This "quantization" of energy levels was a profound departure from classical physics. In the classical view, an atom should be able to absorb any amount of energy — energy is continuous, not laddered. The spectral lines of hydrogen and other elements — the fact that each element emits only certain precise colors of light — were strong circumstantial evidence for Bohr's model. But spectral evidence is indirect: you see the light that comes out when electrons fall back down to lower levels, not the excitation going in.

Energy level — a specific, fixed energy state that an electron in an atom can occupy. Transitions between levels involve the absorption or emission of photons with exactly the right energy. No other energy values are allowed.

What was missing was a direct measurement that showed atoms could only take energy in specific amounts. If you fired particles of controlled kinetic energy at atoms and measured how much energy was transferred, you should see step-like behavior — sharp drops in electron energy at specific thresholds, not smooth energy transfer. Franck and Hertz provided that measurement.

Source: Franck, J. & Hertz, G. (1914), "Über Zusammenstöße zwischen Elektronen und Molekülen des Quecksilberdampfes und die Ionisierungsspannung desselben," Verhandlungen der Deutschen Physikalischen Gesellschaft, 16, 457–467 — the original 1914 paper reporting quantized energy transfer in mercury vapor.

The Apparatus — A Clever Tube

The Franck-Hertz tube is a modified vacuum tube containing a small amount of mercury, which at temperatures above about 115°C produces a vapor at a pressure of around 100 pascals — dense enough for electron-atom collisions to be frequent, thin enough for electrons to travel measurable distances between collisions.

Inside the tube, four elements are arranged in sequence:

The cathode (K): A heated filament that emits electrons by thermionic emission. These electrons start with essentially zero kinetic energy.

The accelerating grid (G₁): A grid held at a small positive voltage to extract electrons from the cathode and give them a low initial energy. This also focuses the electron beam.

The main grid (G₂): A mesh electrode held at voltage V relative to the cathode. Electrons are accelerated through this voltage, gaining kinetic energy of eV (where e is the electron charge). This is the tunable parameter — Franck and Hertz varied this voltage from near zero to above 12 volts and measured what happened to the electron current.

The anode (A): The collector plate, held at a small negative voltage (typically 0.5–1.5 V) relative to G₂. This retarding potential means only electrons with enough kinetic energy upon reaching the G₂ region can make it to the anode against the retarding field.

Source: Franck, J. & Hertz, G. (1914), Verhandlungen der DPG, 16 — apparatus description including tube temperature (115°C), mercury vapor pressure, and electrode configuration.

The logic of the measurement is elegant. If an electron travels from cathode to G₂ without colliding with any mercury atom (or collides only elastically, meaning it bounces without losing energy), it arrives at G₂ with kinetic energy eV and can overcome the small retarding potential to reach the anode — contributing to the measured current. But if the electron undergoes an inelastic collision with a mercury atom — transferring a chunk of energy to the atom — it may arrive at G₂ with insufficient kinetic energy to overcome the retarding potential, and the current to the anode drops.

The key question is: at what electron energies does inelastic energy transfer happen?

What They Observed — the Characteristic Dips

As Franck and Hertz increased the accelerating voltage V from zero upward, they measured the current at the anode. The result was striking.

Below about 4.9 V, the current rose smoothly with voltage, as expected. The electrons were gaining energy but not yet reaching the threshold for exciting mercury atoms.

At approximately 4.9 V, the current dropped sharply.

Then it rose again, before dropping sharply a second time at approximately 9.8 V.

Then it rose again, before dropping at approximately 14.7 V.

The drops occurred at almost exactly 4.9 V, 9.8 V, and 14.7 V — integer multiples of 4.9 eV.

Source: Franck, J. & Hertz, G. (1914), Verhandlungen der DPG, 16, 457 — current-voltage curves showing periodic dips separated by 4.9 V.

The interpretation is straightforward. When an electron has been accelerated to exactly 4.9 eV, it can give all of that energy to a mercury atom in an inelastic collision, exciting the atom's outer electron from its ground state to the first excited level. The projectile electron, now with near-zero kinetic energy, cannot overcome the retarding field and does not reach the anode — the current drops. As the voltage increases further, the electron gains enough energy to excite one atom and still have energy to spare; it reaches the anode again, and the current rises. At 9.8 V, an electron can collide inelastically twice before reaching G₂ — each time giving away 4.9 eV — and the current drops again.

Accelerating Voltage (V)	Number of inelastic collisions	Current behavior
0 – 4.9	0	Rises smoothly
~4.9	1	Sharp drop
4.9 – 9.8	0 after 1st excitation	Rises again
~9.8	2	Second sharp drop
9.8 – 14.7	0 after 2nd excitation	Rises again
~14.7	3	Third sharp drop

This periodic pattern is the experimental fingerprint of a quantized energy level 4.9 eV above the ground state.

The UV Light Confirmation

Franck and Hertz did not stop at the current-voltage curve. They also checked whether the mercury atoms, after being excited, released the absorbed energy as light.

If an atom absorbs exactly 4.9 eV and then returns to the ground state by emitting a photon, the photon's energy must be 4.9 eV. Using E = hf = hc/λ (where c is the speed of light and λ is wavelength), the predicted photon wavelength is:

λ = hc/E = (6.626 × 10⁻³⁴ J·s × 3 × 10⁸ m/s) / (4.9 × 1.602 × 10⁻¹⁹ J) ≈ 253.6 nm

This is deep ultraviolet light, invisible to the eye but detectable with a UV-sensitive detector. Franck and Hertz set up apparatus to detect UV light from the mercury vapor and found emission at exactly 253.7 nm — matching the prediction to within the measurement precision.

Source: Franck, J. & Hertz, G. (1914), Verhandlungen der DPG, 16 — report of UV emission at 253.6 nm coinciding with the current dips, linking the electron energy loss to photon emission from excited mercury atoms.

The two results together — current dips at exact multiples of 4.9 eV and UV emission at 253.7 nm — were a closed loop. Energy went in as kinetic energy of electrons. The same energy came out as ultraviolet light. The atom accepted energy in a specific lump and returned it in a specific photon. Nothing in between was possible.

The Relationship to Bohr's Model — a Historical Irony

Here is the complication that textbooks typically omit: Franck and Hertz did not set out to test Bohr's model, and when they did the experiment in 1914, they were not familiar with Bohr's 1913 paper.

Their interpretation of the 4.9 eV result was initially wrong. They thought the electrons were ionizing the mercury atoms — knocking electrons completely free — and that 4.9 V was the ionization potential of mercury. Ionization and excitation are very different phenomena. Ionization is irreversible removal of an electron from the atom; excitation is a temporary promotion to a higher level followed by return to the ground state.

Bohr read Franck and Hertz's paper and immediately recognized what they had actually measured: the energy of the first excited state of mercury, not the ionization potential. Bohr wrote to Franck and Hertz to explain the correct interpretation.

Source: Jammer, M. (1966), The Conceptual Development of Quantum Mechanics, McGraw-Hill — history of the Franck-Hertz experiment including the initial misinterpretation and Bohr's correction.

Franck and Hertz accepted Bohr's correction and published revised interpretations. What is remarkable is that their data was correct all along. The initial misidentification of 4.9 eV as the ionization potential (the actual ionization potential of mercury is 10.44 eV) was a conceptual error, not a measurement error.

The true ionization potential of mercury would not appear in their apparatus until much higher voltages, and even then the current behavior is different (the current does not recover in the same periodic way). The 4.9 eV dips are unambiguously excitation, not ionization.

What Makes This Experiment Distinctive

Most experiments in atomic physics at this time worked by analyzing spectra — the wavelengths of light emitted by excited atoms. The Franck-Hertz experiment was fundamentally different: it probed the atomic energy structure from the input side, not the output side. Instead of asking "what wavelengths of light does mercury emit," it asked "what kinetic energies of electrons does mercury absorb."

The fact that both approaches gave the same answer — energy levels separated by 4.9 eV — was powerful evidence that the atomic energy levels were real physical quantities, not mathematical artifacts of curve-fitting.

Like the oil-drop experiment's relationship to the electron charge, the Franck-Hertz result gave a direct measurement of something that had previously been inferred. Lenard and others had measured atomic excitation energies through spectroscopy — the 253.7 nm UV line of mercury was known before 1914. Franck and Hertz showed that mechanical energy (electron kinetic energy) and light energy (photon energy) accessed the same underlying structure. The atom does not have one set of levels for light and another for particles; it has one set, period.

Source: Thornton, S. T. & Rex, A. (2013), Modern Physics for Scientists and Engineers, 4th edition, Cengage Learning — standard physics textbook treatment of Franck-Hertz, including the significance of the mechanical vs. optical probing comparison.

Why Mercury? The Practical Logic

Franck and Hertz chose mercury for practical reasons. Mercury is a liquid at room temperature, producing vapor pressure simply by gentle heating. The vapor pressure at 115°C (around 100 Pa) is low enough that electrons can travel centimeters between collisions — crucial for a well-defined beam — but high enough that some fraction of electrons will undergo at least one collision in the length of the tube.

The first excited state of mercury at 4.9 eV is also conveniently low compared to the ionization potential (10.44 eV), creating a large "window" in which excitation can be observed without ionization contaminating the signal. Other elements have their first excited states either too low (making it hard to control the electron energy precisely enough) or too high (requiring very high voltages that complicate apparatus design).

The choice of mercury proved fortuitous in another way: the UV emission at 253.7 nm falls in a spectral region easily distinguished from visible light, making the light output of the excited atoms straightforward to detect and identify.

The Nobel Prize — Delayed by a Decade

Franck and Hertz received the 1925 Nobel Prize in Physics — awarded in December 1926 — "for their discovery of the laws governing the impact of an electron upon an atom." The prize recognized both the 1914 mercury experiment and subsequent work by both physicists expanding the study of electron-atom collisions to other gases and higher energy ranges.

Source: Nobel Committee for Physics (1926), "Nobel Prize in Physics 1925 — Presentation Speech," NobelPrize.org — official citation for Franck and Hertz's prize.

The eleven-year gap between the experiment (1914) and the Nobel Prize reflected the disruption of World War I (both Franck and Hertz served in the German military) and the time needed for the community to fully absorb the result's significance within the developing framework of quantum mechanics. By 1925, Bohr's model had been extended by Sommerfeld, Heisenberg had published the first paper on matrix mechanics, and de Broglie had proposed matter waves. The Franck-Hertz experiment was recognized as one of the foundational results that made all of this possible.

The Modern Franck-Hertz Apparatus

The Franck-Hertz experiment is one of the most widely replicated experiments in undergraduate physics education. Modern versions use neon instead of mercury vapor for pedagogical reasons: neon is non-toxic (mercury vapor requires careful ventilation), and the excitation in neon produces visible light (orange-red glow) that students can see directly rather than relying on UV detection.

In neon, the characteristic energy transfer is approximately 18.7 eV for the main excitation group, corresponding to emission in the visible spectrum. The current-voltage curve shows the same periodic structure as the mercury version, and glowing bands appear inside the tube at the positions where the electrons have just reached the 18.7 eV threshold — a vivid visual demonstration of quantization.

Source: Rapior, G., Sengstock, K., & Baev, V. (2006), "New features of the Franck-Hertz experiment," American Journal of Physics, 74(5), 423–428 — modern analysis of the neon Franck-Hertz tube, including discussion of the multiple excitation levels visible in the current-voltage curve.

Timeline

Year	Event
July 1913	Bohr publishes his model of the hydrogen atom with quantized energy levels
April 24, 1914	Franck and Hertz present their mercury vapor results to the German Physical Society
1914	Franck and Hertz initially interpret 4.9 eV as the ionization potential of mercury
1914–1915	Bohr reads the paper and writes to Franck and Hertz with the correct interpretation (first excited state, not ionization)
1915	Franck and Hertz publish revised interpretation confirming excitation of discrete levels
1914–1918	World War I; both Franck and Hertz serve in German forces
1921	Bohr receives Nobel Prize in Physics for his atomic model
December 10, 1926	Franck and Hertz receive the 1925 Nobel Prize in Physics
1950s–present	Franck-Hertz apparatus becomes standard undergraduate physics laboratory experiment worldwide

The Broader Landscape of Atomic Physics in 1914

To appreciate what Franck and Hertz contributed, it helps to know what was and was not established in atomic physics in 1914. Rutherford had demonstrated the nuclear atom in 1911 — his alpha-particle scattering experiments showed that the atom's positive charge and most of its mass are concentrated in a tiny nucleus. But Rutherford's model was purely structural: a nucleus surrounded by electrons. It said nothing about how electrons were arranged, why atoms were stable (classically, an orbiting electron should radiate energy and spiral into the nucleus within nanoseconds), or why elements emit characteristic spectral lines.

Bohr's 1913 model addressed these questions by combining Rutherford's nuclear atom with Planck's quantum of action. Electrons could only occupy orbits whose angular momentum was a multiple of h/(2π). Jumps between orbits required the emission or absorption of photons with exactly the right energy. The model was wildly successful for hydrogen but was acknowledged to be incomplete even by Bohr — it could not handle multi-electron atoms, and it mixed classical mechanics (orbits) with quantum rules in an ad hoc way.

The community needed experimental tests. Spectroscopy was one avenue, but it probed only the output (emitted photons). Franck and Hertz's method probed the input: how much mechanical energy could be deposited into an atom? The two methods' agreement was powerful cross-validation.

Source: Heilbron, J. L. & Kuhn, T. S. (1969), "The genesis of the Bohr atom," Historical Studies in the Physical Sciences, 1, 211–290 — comprehensive historical account of the development of the Bohr model and the experimental context in which it was received.

Subtleties in the Current-Voltage Curve

The idealized description of the Franck-Hertz curve — a clean periodic oscillation with sharp dips at exactly 4.9, 9.8, 14.7 V — is a simplification. The actual curves are more nuanced, and understanding the deviations illuminates the physics more deeply.

The dips are shifted from simple multiples of 4.9 V. Because the electrode geometry creates a non-uniform electric field inside the tube, electrons gain energy not just between cathode and G₂ but also in the region near G₁. The effective potential seen by an electron depends on where in the tube it undergoes inelastic collisions. Modern analysis of Franck-Hertz curves includes corrections for these geometric effects.

The peaks decrease in height. Later maxima — the second and third peaks — are lower than the first peak. This happens because electrons that have already undergone one inelastic collision have less remaining kinetic energy and are less likely to reach the anode even when slightly above threshold for a second collision.

Temperature affects the curve shape. The mercury vapor pressure is strongly temperature-dependent (rising rapidly above 100°C). At higher temperatures, the electron mean free path is shorter, meaning more collisions occur per unit distance and the current dips appear at lower voltages in the geometric sense, even though the energy threshold is unchanged.

These complications are well understood and are part of what makes the modern Franck-Hertz apparatus a rich quantitative teaching tool, not just a qualitative demonstration.

Source: Rapior, G., Sengstock, K., & Baev, V. (2006), "New features of the Franck-Hertz experiment," American Journal of Physics, 74(5), 423–428 — modern analysis of deviations from the ideal curve, including the role of tube geometry, temperature, and contact potential.

What People Get Wrong About the Franck-Hertz Experiment

"Franck and Hertz designed the experiment to test Bohr's model." They did not know Bohr's model existed when they did the experiment. They were studying electron-atom collisions as part of a broader program of ionization research. The connection to Bohr's model was made by Bohr after the fact.

"They found the ionization energy of mercury." Their initial interpretation was that 4.9 eV was the ionization potential. Bohr corrected this: 4.9 eV is the first excitation energy. The ionization potential of mercury is 10.44 eV.

"The experiment proved Bohr's model." It confirmed that mercury atoms have a discrete energy level at 4.9 eV above the ground state, which is consistent with Bohr's model. But Bohr's model, applied rigorously to mercury (a multi-electron atom), actually gives wrong predictions for most energy levels. The deeper lesson is that energy quantization is real and general, not that Bohr's specific orbital model is correct. The orbital model works well for hydrogen but fails for more complex atoms.

"The current drops to zero at each dip." The dips are minima, not zeroes. Even at the dip voltage, some electrons reach the anode without colliding, and the geometry of the tube means not every electron undergoes an inelastic collision. The current minimum is substantially lower than the adjacent maxima, but it is not zero.

FAQs

Q: What exactly happens to a mercury atom during an inelastic collision in the Franck-Hertz experiment?
A: An outer electron of the mercury atom absorbs exactly 4.9 eV of energy from the colliding electron and jumps to the atom's first excited electronic state. The atom stays in this excited state for roughly 10⁻⁸ seconds (10 nanoseconds), then releases the energy by emitting a photon of UV light at 253.7 nm wavelength and returning to the ground state.

Q: Why do the current dips appear at multiples of 4.9 V rather than only at 4.9 V?
A: At 9.8 V, an electron gains enough energy to excite one mercury atom, lose 4.9 eV, then accelerate again in the remaining voltage gradient and excite a second mercury atom, losing another 4.9 eV. Each additional multiple of 4.9 V allows one additional inelastic collision before the electron runs out of energy. This is why the pattern repeats periodically at 4.9, 9.8, 14.7 V, and so on.

Q: Why does the current recover and rise again between each dip?
A: After each current minimum, the accelerating voltage is slightly above the threshold for one inelastic collision. The electron gives away 4.9 eV to an atom but still has some remaining kinetic energy — enough to overcome the retarding field and reach the anode. As the voltage increases further, this remaining energy grows, and more electrons get through, raising the current until the voltage is high enough for a second inelastic collision.

Q: How does this experiment relate to emission spectra?
A: Both probe the same quantized energy structure but from opposite directions. Emission spectroscopy detects light emitted when excited electrons fall back to lower levels — it measures the energy released. Franck-Hertz measures the energy absorbed mechanically. The 253.7 nm UV line of mercury was already known from spectroscopy before 1914. Franck and Hertz showed that mechanical energy transfer excites the same transition.

Q: What is the significance of 4.9 eV specifically?
A: 4.9 eV is the energy gap between the ground state (6¹S₀) and the first excited state (6³P₁) of the mercury atom's valence electrons. It is a property of mercury's atomic structure — the electrostatic energy difference between two specific electronic configurations. Every atom has its own characteristic set of such gaps, which is why different elements have different spectral lines.

Q: Why was this result important if the hydrogen spectrum already suggested quantization?
A: The hydrogen spectrum showed that light of specific frequencies was emitted, which Bohr explained with quantized levels. But "explaining existing data" is less convincing than "predicting new data from a different method." The Franck-Hertz experiment used a completely different physical mechanism — electron kinetic energy, not photon absorption — to probe the same energy levels and got the same answer. This cross-method consistency is far stronger evidence than any single technique alone.

The Takeaway

Franck and Hertz found, without knowing they were looking for it, that atoms refuse energy they cannot use. An electron carrying 4.8 eV bounces off a mercury atom elastically. An electron carrying 4.9 eV disappears into it — its energy reappearing as an ultraviolet photon 10 nanoseconds later. The boundary is absolute. The experiment was the first mechanical demonstration that Bohr's quantized energy levels were not a mathematical convenience but a physical reality. It also shows something about how science actually works: the most important result in a year of experiments can be one you were not trying to find, interpreted by someone else reading your paper across the continent.

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Read next:

• The Photoelectric Effect Experiment
• The Rutherford Nuclear Atom
• The Davisson-Germer Experiment