AcademyPhotons
Academy
X-Ray Production
Level 1 - Physics topic page in Photons.
Principle
X-rays are produced when fast electrons strike a target. Sudden deceleration produces a continuous bremsstrahlung spectrum, while inner-shell transitions produce characteristic x-ray lines.
The shortest wavelength occurs when one electron gives all of its kinetic energy to one photon.
Notation
\(V\)
accelerating potential
\(\mathrm{V}\)
\(eV\)
electron kinetic energy after acceleration
\(\mathrm{J,\;eV}\)
\(E_\gamma\)
x-ray photon energy
\(\mathrm{J,\;eV}\)
\(\lambda_{\min}\)
minimum x-ray wavelength
\(\mathrm{m}\)
\(\Delta E\)
atomic transition energy
\(\mathrm{J,\;eV}\)
\(f\)
photon frequency
\(\mathrm{s^{-1}}\)
Method
Derivation 1: Accelerate the electron
An electron accelerated through potential difference \(V\) gains kinetic energy \(eV\).
Electron energy
\[K=eV\]
Maximum photon energy
\[E_{\gamma,\max}=eV\]
Derivation 2: Minimum wavelength cutoff
The highest-energy photon has the shortest wavelength.
Photon energy
\[E_\gamma=\frac{hc}{\lambda}\]
Cutoff wavelength
\[\lambda_{\min}=\frac{hc}{eV}\]
Derivation 3: Characteristic lines
If a target atom has an inner-shell vacancy, an outer electron can drop down and emit a photon with energy equal to the level difference.
Characteristic photon
\[hf=\Delta E\]
Characteristic wavelength
\[\lambda=\frac{hc}{\Delta E}\]
Rules
Electron energy
\[K=eV\]
Cutoff wavelength
\[\lambda_{\min}=\frac{hc}{eV}\]
Characteristic photon
\[hf=\Delta E\]
Photon wavelength
\[\lambda=\frac{hc}{E_\gamma}\]
Examples
Question
Electrons are accelerated through
\[25.0\,\mathrm{kV}\]
Find the maximum x-ray photon energy.Answer
The maximum photon energy is
\[E_{\gamma,\max}=25.0\,\mathrm{keV}\]
Checks
- The cutoff wavelength depends on accelerating voltage, not target material.
- Characteristic line energies depend on target material.
- A continuous spectrum comes from many possible electron energy losses.
- A photon cannot carry more energy than the incident electron has.