How does the probability of the photoelectric effect in a medium roughly vary?

The probability of the photoelectric effect in a medium is primarily influenced by the atomic number (Z) of the absorbing material. Specifically, it varies approximately as Z^4. This relationship arises because the photoelectric effect depends on the interaction between the incident photon and the electrons in the atoms of the medium.

As the atomic number increases, the effective number of electrons available for interaction increases, resulting in a higher probability of photon absorption through the photoelectric effect. Additionally, the photoelectric effect is more pronounced for higher atomic number materials because they have higher electron binding energies and more significant effective cross-sections for such interactions.

This relationship underscores why high-Z materials are often used in radiation shielding and imaging applications. Understanding this dependence is vital for medical dosimetry because it helps in selecting appropriate materials for treatment planning and diagnostic imaging in radiology.