On this page
Bohr's model says an atom can only have certain energies. In your textbook that evidence usually comes from spectral lines, which is light coming out of atoms. But can you prove the energy levels another way, by putting energy into atoms and watching what they accept? In 1914 James Franck and Gustav Hertz did exactly that, using little more than a heated wire, a tube of mercury vapour and a meter. This post explains their experiment, works through the numbers, and shows why they almost missed what they had found.
Who were Franck and Hertz?
Both were born in Hamburg. The Nobel facts pages give James Franck's dates as 26 August 1882 to 21 May 1964 and Gustav Hertz's as 22 July 1887 to 30 October 1975. They shared the 1925 Nobel Prize in Physics "for their discovery of the laws governing the impact of an electron upon an atom".
Their Nobel biographies show two very different later lives. Franck directed a physics institute at Göttingen from 1920, resigned in 1933 in protest against the Nazi regime, moved to the United States, and in 1945 helped write the "Franck Report" urging an open demonstration of the atomic bomb instead of its use without warning. Hertz's biography says he was severely wounded in the First World War, later worked in industry at Philips and Siemens, and spent 1945 to 1954 heading a research laboratory in the Soviet Union.
What did the experiment do?
In his Nobel lecture, Franck describes the method. Electrons from a hot wire were accelerated through mercury vapour by a voltage, and the experimenters measured how many electrons still had some energy left after many collisions. A small retarding voltage stopped the slowest ones from being counted.
As the accelerating voltage rose, the current rose too. Then, at a critical voltage, it "falls suddenly to almost zero". Raising the voltage further made it climb again, then fall again, and so on. Franck explains why: "the electrons cannot lose more or less than the critical amount of energy". Below that energy, collisions with mercury atoms are elastic and the electron keeps its energy. At that energy, an electron can hand all of it to an atom, and is left too slow to reach the collector. "The distance between the succeeding maxima gives an exact value of the critical voltage. This is 4.9 V for mercury vapour."
How did they show the energy came back out as light?
If an atom takes in exactly 4.9 eV, it should give it back as a photon of one particular wavelength. Franck notes that this corresponds to the mercury line at 2537 Å in the ultraviolet. When they bombarded the vapour with 4.9 eV electrons, "only the 2,537 Å line appears in the spectrogram", next to the glow of the hot filament. The energy the atom accepted and the light it gave out matched.
Worked example: from 4.9 volts to 253 nm
Use E = hc/λ, so λ = hc/E.
Energy in joules. 4.9 eV × 1.602 × 10⁻¹⁹ J/eV = 7.85 × 10⁻¹⁹ J.
hc. 6.626 × 10⁻³⁴ × 2.998 × 10⁸ = 1.986 × 10⁻²⁵ J m.
Wavelength. 1.986 × 10⁻²⁵ / 7.85 × 10⁻¹⁹ = 2.53 × 10⁻⁷ m = 253 nm.
Shortcut. With hc ≈ 1240 eV nm, λ = 1240 / 4.9 = 253 nm.
Franck's 2537 Å is 253.7 nm. The small gap comes from rounding 4.9.
Now a second question in the same style. An electron is accelerated through 12 V of mercury vapour. What is the largest number of inelastic collisions it can make? Each one costs 4.9 eV, so 12 / 4.9 = 2.4, which means at most 2. After two it keeps 12 − 9.8 = 2.2 eV, too little for a third.
Why did they almost miss the point?
Here is the surprising part. Franck says they first took 4.9 V to be the voltage needed to ionise mercury, not to excite it. Bohr's atomic theory had appeared about half a year before their work was finished, yet, in Franck's words, "We never even mentioned it once in the relevant paper." The correct reading came later, helped by Bohr himself. The real ionisation voltage of mercury was later measured as 10.3 volts, matching what Bohr's theory predicted.
Which mistakes does this help you avoid?
Mixing up excitation and ionisation. Excitation lifts an electron to a higher level inside the atom. Ionisation removes it. Franck and Hertz made this exact mix-up.
Using volts where you need electron-volts. A 4.9 V accelerating voltage gives an electron 4.9 eV, not 4.9 J.
Forgetting the collision is all or nothing. An electron with 6 eV does not give the atom 6 eV. It gives 4.9 eV and keeps 1.1 eV.
The JEE (Main) 2026 syllabus lists the Bohr model, energy levels and the hydrogen spectrum, and the same E = hc/λ step appears in our hydrogen spectrum problems. Check the syllabus for your exam year.
If you can follow each step but cannot see which to do first in a new problem, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
What can a student take from Franck and Hertz?
Simple apparatus, clear question. A wire, a tube and a meter tested the deepest idea of the day.
Data can outrun interpretation. Their numbers were right before their explanation was. Keep results separate from what you think they mean.
Admit the miss. Franck used his Nobel lecture to say plainly what they got wrong.
Next step: repeat the worked example for helium, whose critical voltage Franck puts at about 20 V, and find the wavelength.
