Franck-Hertz Experiment

In 1914, James Franck and Gustav Hertz performed a landmark experiment that provided direct experimental proof that atoms can only absorb energy in discrete, specific amounts — confirming the quantum model of the atom. Before their work, Bohr's model of quantised energy levels was largely theoretical; the Franck-Hertz experiment made those energy levels observable in the laboratory, earning Franck and Hertz the Nobel Prize in Physics in 1925. The experiment works by firing electrons through a tube of mercury vapour and measuring how much energy the electrons transfer to the mercury atoms. Instead of transferring any arbitrary amount of energy (as classical physics would predict), the electrons only transfer energy in fixed chunks — exactly the amounts needed to bump a mercury electron from one energy level to a higher one. This is analogous to a ball that can only climb a staircase in whole steps: it cannot stop halfway between steps. The signature result is a periodic dip in the electric current collected at the detector every time the accelerating voltage increases by about 4.9 V. Each dip corresponds to electrons gaining just enough kinetic energy to excite a mercury atom, losing that energy in the collision, and then being unable to reach the collector. This repeating pattern is unmistakable evidence that atomic energy levels are quantised, not continuous.

Key takeaways
  • The Experimental Setup
  • Elastic vs. Inelastic Collisions
  • The Current Dips
  • The Emitted Ultraviolet Photon

The Experimental Setup

The tube contains mercury vapour at low pressure. A heated cathode (K) emits electrons by thermionic emission. An accelerating grid (G) is held at a positive voltage V relative to the cathode, pulling electrons through the vapour. A collector plate (A) is held at a small retarding voltage (about 1.5 V) below the grid potential, so only electrons with sufficient kinetic energy after the grid can reach it and register as current.

Elastic vs. Inelastic Collisions

At low accelerating voltages, electrons collide with mercury atoms but bounce off elastically — they transfer negligible kinetic energy because they are so much lighter than the mercury atom (analogous to a ping-pong ball bouncing off a bowling ball). As voltage increases, electrons gain more kinetic energy. When an electron's kinetic energy reaches exactly 4.9 eV, it can collide inelastically with a mercury atom, transferring exactly 4.9 eV to excite the atom from its ground state to its first excited state.

The Current Dips

After an inelastic collision at the grid, the electron has given away (almost) all its kinetic energy and can no longer overcome the retarding voltage. Current at the collector drops sharply. As voltage increases beyond 4.9 V, electrons again have enough residual energy to reach the collector, and current rises — until the voltage is high enough that electrons can undergo two inelastic collisions (at ~9.8 V), causing a second dip. This produces the characteristic periodic current-voltage graph with minima spaced 4.9 V apart.

The Emitted Ultraviolet Photon

After an inelastic collision, the mercury atom is in an excited state. It quickly returns to its ground state by emitting a photon of ultraviolet light. Using E = hf, a 4.9 eV energy drop corresponds to a wavelength of about 254 nm — ultraviolet light. Franck and Hertz observed exactly this UV emission from the tube, providing independent confirmation of the energy-level transitions.

The Key Equation

Ephoton=hf=hcλ=eVexcitationE_{\text{photon}} = hf = \frac{hc}{\lambda} = eV_{\text{excitation}}
  • E_{\text{photon}} — Photon energy (eV or J): The energy carried by the photon emitted when the mercury atom returns to its ground state.
  • h — Planck's constant (J·s): The fundamental quantum of action, h = 6.626 × 10⁻³⁴ J·s.
  • f — Frequency of emitted light (Hz): The frequency of the ultraviolet photon emitted by mercury during de-excitation.
  • e — Elementary charge (C): The charge of one electron, e = 1.602 × 10⁻¹⁹ C.
  • V_{\text{excitation}} — Excitation voltage (V): The accelerating potential at which inelastic collisions first occur; 4.9 V for mercury's first excited state.

Worked Example

Problem. In the Franck-Hertz experiment with mercury vapour, the first excitation potential is 4.9 V. (a) Calculate the energy in joules transferred to a mercury atom during one inelastic collision. (b) Calculate the wavelength of the ultraviolet photon subsequently emitted by the mercury atom.

λ=hceV=(6.626×10−34)(3.00×108)(1.602×10−19)(4.9)≈254 nm\lambda = \frac{hc}{eV} = \frac{(6.626\times10^{-34})(3.00\times10^8)}{(1.602\times10^{-19})(4.9)} \approx 254\text{ nm}

Answer. The energy transferred is 7.85 × 10⁻¹⁹ J, and the emitted photon has a wavelength of approximately 254 nm (ultraviolet).

Figure
Diagram
Franck-Hertz Experiment: Current vs. Accelerating VoltageAccelerating Voltage V (volts)Collector Current I04.99.814.719.61st dip2nd dip3rd dipMinima spaced 4.9 V apart= first excitation energy of HgE = 4.9 eV → λ ≈ 254 nm (UV)
Origins · 1 minJames Franck and how this was discovered
JF
James Franck
1882–1964 · German-American

James Franck, together with Gustav Hertz, designed and carried out the 1914 experiment demonstrating that electrons transfer energy to atoms only in discrete, quantised amounts. Their work provided crucial direct evidence for Bohr's atomic model and the concept of quantised energy levels. Both men were awarded the Nobel Prize in Physics in 1925 for this discovery. Franck was a decorated artillery officer in World War I, yet he later became a passionate pacifist and was one of the first Jewish scientists to resign from his German university position in protest when the Nazis came to power in 1933. He moved to the United States and eventually worked on the Manhattan Project, where he led the 'Franck Report' committee that argued — unsuccessfully — against using the atomic bomb on civilian targets.

  • Bohr Model of the Atom — The Franck-Hertz experiment directly confirmed Bohr's postulate that electrons occupy discrete energy levels; understanding the Bohr model gives theoretical context to the experimental results.
  • Photoelectric Effect — Like the Franck-Hertz experiment, the photoelectric effect demonstrated that energy is exchanged in discrete quanta; both are foundational experiments of the quantum revolution.
  • Atomic Emission Spectra — The UV photons emitted by mercury atoms after Franck-Hertz collisions are an example of line emission spectra; both phenomena arise from electrons transitioning between fixed energy levels.
  • de Broglie Wavelength — The electrons used in the Franck-Hertz experiment have wave-like properties; de Broglie's hypothesis provides the quantum mechanical foundation for why atomic energy levels are discrete.