Question

When X-rays interact with matter, in which of the following situations, the chances of photoelectric effect are more?

• A. X-ray photon having slightly higher energy than the binding energy of inner shell electrons of the atom
• B. X-ray photon having slightly higher energy than the binding energy of inner shell electron, interacting with outer shell electrons of the atom
• C. X-ray photon having much higher energy than the binding energy of inner shell electron, interacting with outer shell electrons of the atom
• D. X-ray photon having much higher energy than the binding energy of inner shell electron, interacting with inner shell electrons of the atom

Hint:

The sharp increase in photoelectric absorption that occurs when the photon energy exceeds the binding energy of a specific shell is called the absorption edge (e.g., K-edge).
This is why contrast agents like iodine and barium work so well; their K-shell binding energies match diagnostic X-ray energies perfectly.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
When an X-ray beam passes through an animal's body, the photons interact with the atoms of the tissues.
The three primary interaction mechanisms in diagnostic radiology are coherent scattering, Compton scattering, and the photoelectric effect.
The photoelectric effect is responsible for creating useful radiographic contrast because it involves the complete absorption of the X-ray photon.

Step 2: Detailed Explanation:
Let us analyze the conditions that maximize the probability of the photoelectric effect:
- For a photoelectric interaction to occur, the incident X-ray photon must have sufficient energy to overcome the binding energy of an inner-shell electron (usually the K or L shell).
- The probability of this interaction is highest when the energy of the incident photon is equal to or slightly greater than the binding energy of the inner-shell electron.
If the photon's energy is lower, it cannot eject the inner-shell electron.
If the photon's energy is much higher, the probability of photoelectric absorption decreases rapidly (it is inversely proportional to the cube of the photon's energy, \(1/E^3\)), and Compton scattering becomes the dominant interaction.
- Therefore, a photon with an energy slightly higher than the binding energy interacting with an inner-shell electron provides the optimal conditions for photoelectric absorption.

Step 3: Final Answer:
The chances of the photoelectric effect are highest when the X-ray photon has slightly higher energy than the binding energy of inner shell electrons of the atom.