Physics
Davisson-Germer
Electrons diffract off a nickel crystal: a peak at 50 degrees for 54 volts, from de Broglie's wavelength and one lattice constant. The measurement that made matter waves real.
What happens
Electrons are fired at a nickel crystal and come back as a wave: de Broglie's λ = h/√(2meV) together with one lattice constant puts the first-order maximum at 50.9° for 54 volts, and Davisson and Germer measured 50°. Nothing is tuned - turn the voltage and the peak walks exactly where d·sin φ = λ puts it, and the module finds it by scanning the curve rather than reading it off the formula that placed it. Below 32.5 V the wavelength exceeds the atom spacing, there is no first order at all, and that is reported instead of a peak jammed against the edge; the faint curve underneath is what particles bouncing off a rough surface would give - a smooth lobe with no maximum anywhere.
Equations used in the module
Equations λ = h / p = h / √(2 m e V) (de Broglie) n λ = 2 d sin θ (Bragg); nickel d = 0.091 nm 54 V → λ = 0.167 nm → peak at 50° the two scans (twin): I(θ) at 54 V peaks at 50.92°, 2.057 on a classical 0.507; I(V) at 50° peaks where the first order passes the detector, V* = h²/(2me·d²·sin²50°) = 55.45 V, half maximum 47.5…67.0 V; threshold h²/(2me·d²) = 32.54 V
