5.9
V
15.7
V
4.9
V
7.850666e-19
J
253.03
nm
14.7
eV
5.9
V
15.7
V
4.9
V
7.850666e-19
J
253.03
nm
14.7
eV
The Franck-Hertz Calculator helps analyze the classic Franck-Hertz experiment, which provided direct experimental evidence for the quantization of atomic energy levels. James Franck and Gustav Hertz performed their landmark experiment in 1914 (Nobel Prize 1925), demonstrating that atoms can only absorb discrete amounts of energy corresponding to transitions between quantized energy levels.
In the Franck-Hertz experiment, electrons are accelerated through a gas (classically mercury vapor, now often neon) by an applied voltage. Below a threshold voltage corresponding to the first excitation energy of the gas atoms, electrons travel from cathode to anode and the current increases smoothly. At the threshold voltage, electrons have just enough energy to excite gas atoms through inelastic collisions, losing their kinetic energy and failing to reach the collector — the current drops sharply.
As the accelerating voltage increases further, electrons regain enough energy after one collision to reach the collector, and current rises again. Another dip occurs when electrons have enough energy to make two inelastic collisions. The result is a characteristic current-voltage curve with equally spaced current dips, each separated by the first excitation energy of the gas in electron-volts.
For mercury, the first excitation energy is 4.9 eV, producing current dips every 4.9 V. For neon, the first excitation energy is about 18.7 eV. After excitation, atoms return to the ground state by emitting photons of the corresponding energy, producing visible light in a spatial pattern matching the regions of maximum inelastic collision.
The Franck-Hertz experiment is remarkable for demonstrating quantization directly through macroscopic electrical measurements, without requiring optical spectroscopy. It remains a standard undergraduate laboratory experiment in modern physics curricula.
Current dips occur at voltages V_n = n * E_excitation + V_contact, where n is the dip number (1, 2, 3...), E_excitation is the first excitation energy in eV, and V_contact is the contact potential offset (typically 0.5-2 V for mercury). The spacing between consecutive dips equals E_excitation in volts. The photon emitted upon de-excitation has wavelength lambda = hc/E = 1240/E(eV) nm.
The equal spacing of current dips (each separated by the excitation energy in volts) is the key signature of quantized energy levels. For mercury (4.9 eV), dips appear at approximately 5.9, 10.8, 15.7, 20.6 V (with 1 V contact potential). The emitted photon wavelength for mercury is 254 nm (UV). For neon the light is visible red-orange around 585-640 nm.
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Mercury shows dips at 5.9 V, 10.8 V, and 15.7 V. The de-excitation photon at 253 nm is deep UV, responsible for the germicidal properties of mercury UV lamps.
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Neon requires 18.7 eV for its first excitation, with dips around 20 and 39 V. The orange-red light emission makes the dip positions visible as luminous bands in the tube.
It provided direct proof that atomic energy levels are quantized. Electrons can only transfer specific discrete amounts of energy to atoms, demonstrating that atoms exist in discrete energy states.
Because each inelastic collision transfers exactly one excitation energy worth of kinetic energy from the electron to the atom. Each additional quantum of accelerating voltage allows the electron to make one more collision.
The difference in work functions between the cathode and anode materials creates a built-in potential offset, shifting all dip positions by a constant voltage. It does not affect the spacing between dips.
Mercury has a low excitation energy (4.9 eV) accessible with modest accelerating voltages, and is a liquid at room temperature making it easy to use as a vapor. Its 254 nm UV emission is also historically significant.
Mercury emits 254 nm UV light (invisible). Neon emits visible orange-red light around 585-640 nm from its excited states, making the collision regions visible as glowing bands.
At lower voltages electrons carry less kinetic energy than the first excitation energy. Elastic collisions (no energy transfer) are possible but inelastic collisions (energy transfer) cannot occur — energy conservation forbids partial quantum jumps.
Between dips the current rises as the accelerating voltage gives electrons more kinetic energy after their last inelastic collision, allowing more electrons to overcome the small retarding field and reach the collector.
In principle yes, but higher excitations require greater voltages and the cross-section (probability) for different transitions varies. The first excitation typically dominates the pattern of dips.
It confirmed Bohr's 1913 prediction of discrete atomic energy levels independently of optical spectroscopy. The 4.9 eV result for mercury agreed with the known UV spectral line at 254 nm (hc/lambda = 4.9 eV).
Yes, it remains a standard undergraduate physics laboratory experiment. Modern versions often use neon (safer than mercury vapor) and computer-based data acquisition to display the characteristic current-voltage curve.
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