22.5 Electron Diffraction, Bragg Geometry, and Quantised Orbits

Electron beams scattered by crystalline nickel show intensity maxima at specific angles, exactly like wave interference from layered scattering centers. These angular peaks cannot be explained by random particle bounce distributions alone. They match path-difference conditions for constructive interference when interplanar geometry and de Broglie wavelength are combined.

Experimentally, once kinetic energy sets electron wavelength through h/p, measured peak angles can be predicted. Or equivalently, measured angles can be used to infer wavelength and compared with de Broglie prediction. Agreement between these independent routes is what gives strong confidence in matter-wave interpretation.

Always run a feasibility check before solving for angle: n lambda/(2d) must be less than or equal to 1. If it exceeds 1, that order is not physically allowed for that wavelength and spacing. This simple inequality is often faster than full trigonometric calculation and prevents impossible results.

This standing-wave picture provides intuition for why only discrete radii/energies are stable in early quantum models: if circumference does not fit an integer number of wavelengths, destructive self-interference prevents a stationary wave pattern. While full quantum mechanics replaces Bohr orbits with orbitals and wavefunctions, this relation remains a powerful conceptual bridge.