Photoelectric Effect

1. The Photoelectric Effect

The photoelectric effect, also known as the 'photoeffect', occurs when a photon interacts with a tightly bound orbital electron in an absorber atom. The photon is absorbed, and the electron is ejected as a photoelectron. The kinetic energy \( E_K \) of the emitted photoelectron is given by the equation:

Where:

• \( E_K \) is the kinetic energy of the photoelectron.
• \( h\nu \) is the energy of the incident photon.
• \( E_B \) is the binding energy of the ejected electron (i.e., the energy required to remove the electron from the atom).

For the photoelectric effect to take place, the photon energy \( h\nu \) must exceed the binding energy \( E_B \) of the electron. The closer \( h\nu \) is to \( E_B \), the higher the probability of the photoelectric effect occurring.

Fig. 1.6: Fluorescence yields \( \omega_K \), \( \omega_L \), and \( \omega_M \), and the probabilities for the Auger effect \( 1 - \omega \), against atomic number \( Z \) of the absorber. Data from the NIST.

2. Photoelectric Mass Attenuation and Absorption Edges

The photoelectric mass attenuation coefficient \( \frac{\mu_\tau}{\rho} \) represents how much a photon beam is attenuated per unit mass of the absorbing material. This coefficient depends on the photon energy \( h\nu \) and the atomic number \( Z \) of the absorbing material. At low photon energies, the photoelectric effect dominates photon attenuation.

The coefficient exhibits sharp discontinuities, called absorption edges, which occur when the photon energy \( h\nu \) becomes equal to the binding energy \( E_B \) of an atomic shell. For instance, in lead, the K absorption edge occurs when \( h\nu = 88 \, \text{keV} \) because the K-shell binding energy in lead is 88 keV.

3. Mathematical Relationship

The photoelectric attenuation coefficient \( \frac{\mu_\tau}{\rho} \) varies approximately as:

This shows that the probability of the photoelectric effect increases with the atomic number \( Z \) and decreases with the cube of the photon energy \( h\nu \). The mass attenuation coefficient also follows a similar dependence:

At relatively low photon energies, where \( h\nu \) is around the binding energy of the K shell and less than 0.1 MeV, the photoelectric effect contributes significantly to the overall photon attenuation. However, at higher photon energies, the Compton scattering and pair production mechanisms become the dominant contributors to photon attenuation.

4. Example Calculation