When an electron collides with an atom, will the atom accept any amount of energy (as a classical object should) — or only specific lumps?
▶ Launch the interactive simulationFire electrons through mercury vapour, accelerated by a voltage V, past a small retarding potential V_r to a collector. Forward-model the collector current from energy bookkeeping: an electron excites a Hg atom (dumping E_exc = 4.9 eV) each time its running kinetic energy reaches that lump, and reaches the collector only if its residual energy clears V_r. Sample the I–V curve, detect the current dips, and least-squares fit each dip voltage against its index n.
the excitation energy E_exc = 4.90 eV — recovered as the SLOPE of a single straight line through the equally-spaced current dips (the dips repeat every 4.9 V because the mercury atom takes ONLY the one lump that lifts it 6¹S₀→6³P₁, never any energy offered); the de-excitation light λ = hc/E_exc = 254 nm, exactly the mercury UV resonance line Franck & Hertz saw the tube glow with; and from it Planck's constant h = E_exc·e·λ/c, the SAME h the blackbody, photoelectric, hydrogen, Compton and de Broglie worlds give. A classical atom, able to absorb a little from every collision, would give a smooth dip-free current — the dips exist only because energy comes in steps. Franck & Hertz's 1914 result (Nobel 1925), the direct collisional confirmation of Bohr's quantized levels and the sixth pillar of early quantum theory