Modern physics
X-rays
Duane–Hunt limitλmin = hc/eVmax photon energy = eV
X-ray spectrum (Mo target)
Continuous bremsstrahlung with sharp cutoff at λmin — Kα/Kβ characteristic lines above 20 kV
Parameters
Tube voltage35 kV
Higher V → shorter λmin → harder, more penetrating X-rays
Filament current5
More electrons → more X-rays, but λmin does not move
Calculated
λmin0.0355 nm
Max photon energy35 keV
Electron KE35 keV
K linesvisible
Energy → heat~99 %
Curriculum
WAECNECOIGCSESATJUPEB
📋 Teacher notes
- •X-ray production is the photoelectric effect in REVERSE: fast electrons in, photons out. Electrons accelerated through kV strike a metal target; ~99% of their energy becomes heat, ~1% becomes X-rays (which is why anodes are cooled or rotated).
- •The continuous (bremsstrahlung = "braking radiation") spectrum has a sharp cutoff λmin = hc/eV — the Duane–Hunt limit. An electron cannot give a photon more than its whole kinetic energy eV.
- •Raise the tube voltage: λmin slides LEFT (shorter, more penetrating "harder" X-rays). Raise the filament current: MORE X-rays (taller spectrum), same λmin.
- •The sharp Kα/Kβ characteristic lines appear only when electrons can knock out inner-shell electrons of the target (Mo: above ~20 kV). Their wavelengths identify the target element — the basis of X-ray spectroscopy.
- •Properties for exams: travel in straight lines, not deflected by electric/magnetic fields (uncharged), ionise gases, penetrate matter (absorbed by dense material like bone/lead), affect photographic film.
✏️ Exercises