Duane-Hunt limit

The Duane-Hunt limit is the sharp upper-energy cutoff in the bremsstrahlung continuum produced by an X-ray tube: no photon in the continuous spectrum has energy greater than E_max = eU, where U is the voltage across the tube and e is the electron charge. Equivalently, the spectrum has a minimum wavelength λ_min = hc/(eU) — above which X-rays are found, below which there are none. A tube running at U = 50 kV produces no photons above 50 keV; a 100 kV tube cuts off at 100 keV; every tube cuts off exactly at the accelerating voltage. The cutoff is not a gradual falloff but an absolute wall in the spectrum, verifiable with a Bragg-crystal spectrometer to within the resolution of the instrument.

The interpretation is direct energy conservation at the quantum level. An electron entering the target with kinetic energy eU cannot radiate more energy in a single photon than it brought in. In the most extreme single scattering event the electron gives all its kinetic energy to one bremsstrahlung photon, producing hν_max = eU, i.e. the Duane-Hunt limit. Discovered experimentally by William Duane and Franklin Hunt at Harvard in 1915 — one year after Moseley's X-ray spectroscopy established that atomic X-ray lines depended on Z² — the limit was one of the earliest laboratory demonstrations outside the photoelectric effect that photon energy is quantised as E = hν, with h the same Planck constant that appeared in blackbody radiation and the Bohr atom. Rearranged, the relation λ_min·U = hc/e ≈ 1.2398 keV·nm / (kV) gives a precision determination of the ratio h/e; modern measurements use the same relation at the 10⁻⁹ level to tie macroscopic voltage standards to atomic physics via the Josephson effect.

Discovered by William Duane and Franklin Hunt at Harvard in 1915, in what was one of the first confirmations of E = hν outside Einstein's photoelectric-effect theory.