24.2.1 Production of X-Rays

X-rays

X-rays

X-rays are electromagnetic waves which have wavelengths in the range $10^{-8}$ to $10^{-13}$ $\text{m}$

Producing X-rays

X-ray tube setup

Generation of X-rays in an X-ray tube

• Electrons are emitted from the heated cathode by thermionic emission.
• The electrons are accelerated towards the anode by a large potential difference.
• Electrons bombard the metal target and decelerate.
• Some of their kinetic energy is converted into energy of X-ray photons.

Minimum Wavelength

Maximum Energy Gained by Electrons

• When an electron is accelerated across a potential difference $V$ it gains kinetic energy equal to: $E_K=eV$

Minimum Wavelength of X-ray Photons

• Since some of the kinetic energy of the electrons are converted into X-ray photons, the maximum energy an X-ray photon can have is equal to the maximum kinetic energy of the electrons: $\frac{hc}{\lambda }=eV$ $\lambda =\frac{hc}{eV}$

X-ray Spectrum

X-ray Emission Spectrum

X-ray spectrum

Continuous Distribution

• An X-ray photon is produced when an electron is decelerated.
• Larger acceleration results in larger photon energy.
• Photon energy is related to wavelength
• Electrons hitting the metal target have a continuous range of accelerations.
• Therefore they produce a continuous spectrum of wavelengths.

Sharp cut-off at short wavelength

• Electron gives all its energy to one photon and is stopped in a single collision

Superimposed Peaks on the Continuous Distribution of Wavelengths

• De-excitation of orbital electrons in the metal target emit photons whose energy is equal to the difference in energy levels.