= Franck-Hertz experiment
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{wiki=Franck–Hertz_experiment}
The Franck-Hertz experiment connects a reproducible loss of <Electron> <kinetic energy> with excitation of a <chemical atom>. The original mercury-vapor experiments were performed during 1912–1914 while investigating <ionization>; they were not designed as a test of the <Bohr model>. Their later interpretation distinguished internal excitation from removal of an <Electron>. https://labs.physik.kit.edu/prakt-klass-physik-manuals/P2/Franck_Hertz_Versuch/[KIT physics laboratory, H23 Franck-Hertz-Versuch, Motivation]{ref}.
In a modern mercury tube, a heated <cathode> emits <Electrons> and a positive perforated grid accelerates them through Hg vapor. A collector slightly below the grid's <electric potential> rejects slow <Electrons>. The oven controls vapor density and hence the <mean free path>. Keep heating and retarding settings fixed, sweep the accelerating <electric potential difference> $V$, and record collector <electric current> $I(V)$. These measured quantities indirectly probe atomic excitation. https://physlab.org/wp-content/uploads/2016/03/Franck_exp_v12015.pdf[Shah, Alam and Anwar, Electron energy loss investigated through the Franck-Hertz Experiment, sections 3–4]{ref}.
The curve shows repeated current minima, typically about $4.9\,\mathrm V$ apart. In the collision model, an <Electron> gains approximately $eV$ of <kinetic energy>, with $e$ the positive <elementary charge>. An <inelastic collision> transfers about $4.9\,\mathrm{eV}$ to internal excitation. Near the grid, this can prevent the <Electron> crossing the retarding region, lowering collected <electric current>. Further acceleration restores collection; repeated excitation losses produce further minima. These represent multiple collisions, rather than equally spaced atomic <energy eigenvalues>. Contact potentials shift the first minimum, so compare several successive spacings instead of identifying the first dip's voltage with the excitation cost. https://physlab.org/wp-content/uploads/2016/03/Franck_exp_v12015.pdf[Shah, Alam and Anwar, sections 3.1–4 and Figure 3]{ref}.
The optical comparison supplies a second observable: mercury radiation at a <wavelength> near $253.6\,\mathrm{nm}$ was detected through a window in the tube. Its inferred <photon> <energy> $hc/\lambda\approx4.89\,\mathrm{eV}$ agrees with the characteristic collision loss, with $c$ the <speed of light>. This agreement supports the interpretation as a transition between internal atomic energies. It does not make the collector trace a complete spectrum. In particular, the lowest excited mercury level, labeled $6\,{}^3P_0$, is metastable because an <electric-dipole selection rule> forbids its direct transition to the <ground state>; the nearby $6\,{}^3P_1$ level emits the quoted <ultraviolet> line. Collision excitation and optical detection therefore have different sensitivities to the available <excited states>. https://ocw.mit.edu/courses/8-13-14-experimental-physics-i-ii-junior-lab-fall-2016-spring-2017/afdfff9f8bbe067239af19c8b178a764_MIT8_13-14F16-S17exp7.pdf[MIT Junior Lab, The Franck-Hertz Experiment, section VI and the discussion following Figure 6]{ref}.
Initial <Electron> <kinetic energy> spread and varying collision positions broaden real minima. Repeat traces at different retarding settings and oven temperatures to distinguish excitation from collection effects. This probes a discrete energy-transfer channel, rather than every <energy eigenspace>, its <dimension>, or an absolute <ground-state energy>. https://ocw.mit.edu/courses/8-13-14-experimental-physics-i-ii-junior-lab-fall-2016-spring-2017/afdfff9f8bbe067239af19c8b178a764_MIT8_13-14F16-S17exp7.pdf[MIT Junior Lab, sections IV and VI]{ref}.
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