What does the Franck–Hertz experiment prove?

It shows that atoms absorb energy in discrete amounts. Below 4.9 eV electrons collide elastically with mercury atoms and lose almost nothing; at 4.9 eV they can excite an atom to its first excited state, lose 4.9 eV and can no longer climb the retarding voltage to the anode, so the current drops. Each extra 4.9 V or so allows one more excitation, giving evenly spaced peaks and dips, the first direct evidence for Bohr’s energy levels (1914).

Why is the first peak not at 4.9 V?

The cathode and grid are made of different metals, so there is a contact potential of about 1–2 V; together with the retarding voltage and the distance an electron travels past threshold before colliding, this shifts the whole curve to the right and the first peak often sits at 6–7 V. That is why the spacing between neighbouring peaks (or dips), not the position of the first peak, gives the excitation potential.

How does the oven temperature change the curve?

The temperature sets the mercury vapour pressure and hence the electron mean free path. Hot: short paths, electrons collide just past threshold, so the dips are sharp and deep but more scattering lowers the current. Cold: long paths, electrons keep gaining energy past threshold, the structure washes out, and they may reach the 10.4 eV ionization energy and make the tube discharge. Mercury tubes usually run at 170–200 °C.

How is the excitation energy related to the emitted light?

An excited mercury atom quickly returns to the ground state and emits a photon with the excitation energy: λ = hc/E₁ = 1239.84 nm·eV / 4.887 eV ≈ 253.7 nm, mercury’s ultraviolet resonance line, which Franck and Hertz later observed directly. Neon’s excitation energy is about 18.7 eV; those states first decay to the lower 3s levels, emitting 585–640 nm orange-red light, so you can see glowing layers in a neon tube that multiply as the voltage rises.

Why are higher-order spacings slightly larger than 4.9 V?

An electron that reaches threshold does not collide at once; on average it travels one more inelastic mean free path and gains extra energy on the way, and that extra grows with the field, i.e. with the accelerating voltage. So the spacing increases a little with order; a careful 2006 measurement found an increase of order 0.1 V per step. The Monte Carlo model reproduces this, visible as a systematic trend in the fit residuals.

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🔦Franck–Hertz Experiment Simulator - I–V curve, excitation energy, levels

A simulated Franck–Hertz tube: electrons leave the cathode, are accelerated towards the grid and collide with mercury (or neon) atoms, and once they reach the first excitation energy they can excite an atom and lose that energy. The tool follows thousands of electrons with a Monte Carlo model and plots the anode current I_A against the accelerating voltage, with peaks and dips about 4.9 V apart for mercury or about 19 V for neon. Oven temperature, retarding voltage and filament voltage are adjustable, showing how the mean free path shapes the curve. Pick the peaks or find them automatically and a linear fit gives the spacing, the excitation energy and the photon wavelength of 253.7 nm.

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Franck–Hertz Experiment Simulator

1Choose the mercury or neon tube, drag the accelerating voltage or press Auto sweep and watch the electrons and the I–V curve
2Adjust oven temperature (or neon pressure), retarding voltage and filament voltage and compare the dips and the total current
3Press Find peaks, or click the curve to add or remove peaks
4Read the peak spacing ΔU from the linear fit and successive differences, the energy E₁ and the wavelength λ = hc/E₁

FAQ

What does the Franck–Hertz experiment prove?: It shows that atoms absorb energy in discrete amounts. Below 4.9 eV electrons collide elastically with mercury atoms and lose almost nothing; at 4.9 eV they can excite an atom to its first excited state, lose 4.9 eV and can no longer climb the retarding voltage to the anode, so the current drops. Each extra 4.9 V or so allows one more excitation, giving evenly spaced peaks and dips, the first direct evidence for Bohr’s energy levels (1914).
Why is the first peak not at 4.9 V?: The cathode and grid are made of different metals, so there is a contact potential of about 1–2 V; together with the retarding voltage and the distance an electron travels past threshold before colliding, this shifts the whole curve to the right and the first peak often sits at 6–7 V. That is why the spacing between neighbouring peaks (or dips), not the position of the first peak, gives the excitation potential.
How does the oven temperature change the curve?: The temperature sets the mercury vapour pressure and hence the electron mean free path. Hot: short paths, electrons collide just past threshold, so the dips are sharp and deep but more scattering lowers the current. Cold: long paths, electrons keep gaining energy past threshold, the structure washes out, and they may reach the 10.4 eV ionization energy and make the tube discharge. Mercury tubes usually run at 170–200 °C.
How is the excitation energy related to the emitted light?: An excited mercury atom quickly returns to the ground state and emits a photon with the excitation energy: λ = hc/E₁ = 1239.84 nm·eV / 4.887 eV ≈ 253.7 nm, mercury’s ultraviolet resonance line, which Franck and Hertz later observed directly. Neon’s excitation energy is about 18.7 eV; those states first decay to the lower 3s levels, emitting 585–640 nm orange-red light, so you can see glowing layers in a neon tube that multiply as the voltage rises.
Why are higher-order spacings slightly larger than 4.9 V?: An electron that reaches threshold does not collide at once; on average it travels one more inelastic mean free path and gains extra energy on the way, and that extra grows with the field, i.e. with the accelerating voltage. So the spacing increases a little with order; a careful 2006 measurement found an increase of order 0.1 V per step. The Monte Carlo model reproduces this, visible as a systematic trend in the fit residuals.

Features

Electron-by-electron Monte Carlo: uniform acceleration, excitation probability above threshold, loss of E₁ per collision, collection against the retarding field
Mercury vapour pressure vs oven temperature, with electron and excitation mean free paths
Animated electrons in the tube with flashes at each excitation; glowing layers in the neon tube that multiply with voltage
I–V curve with a voltage cursor and an X–Y-recorder style sweep
Automatic or manual peak picking, linear fit and successive differences for ΔU, E₁ and the photon wavelength
Discharge warning, and explanations of the contact potential and the slowly growing peak spacing

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