Energy of the x-ray photonThe probability of photoelectric interactions is highest when the x-ray photon energy is slightly above the electron binding energy. If the photon energy is too low it cannot free the electron. If the energy is too high the probability of an interaction significantly decreases due to the inverse relationship with the cube of the energy as demonstrated in the equation for the photoelectric LAC.
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The photoelectric effect, a.k.a. photoelectric absorption, is one of the principal forms of interaction of x-ray and gamma photons with matter. A photon interacts with an inner shell electron in the atom and removes it from its shell. Probability of photoelectric effectThe probability of this effect is maximum when:
The electron that is removed is then called a photoelectron and the incident photon is completely absorbed in the process. Hence, the photoelectric effect contributes to the attenuation of the x-ray beam as it passes through matter. To stabilize the atom an outer shell electron fills the vacancy in the inner shell. The energy which is lost by this electron as it drops to the inner shell is emitted as characteristic radiation (an x-ray photon) or as an Auger electron. The probability of photoelectric absorption occurring is
Thus the overall the probability of photoelectric absorption can be summarized as follows: Photoelectric absorption ~ p·(Z³/E³) Therefore if Z doubles, photoelectric absorption will increase by a factor of 8 (2³ = 8), and if E doubles photoelectric absorption will reduce by a factor of 8. Small changes in Z and E can therefore significantly affect photoelectric absorption. This has practical implications in the field of radiation protection and is the reason why materials with a high Z such as lead (Z = 82) are useful shielding materials. Photoelectric absorption is also utilized in mammography and when using contrast agents to improve image contrast. The dependence of photoelectric absorption on Z and E means that it is the major contributor to beam attenuation up to approximately 30 keV when human tissues (Z = 7.4) are irradiated. At beam energies above this, the Compton effect predominates.
The electron range in other materials can be determined by dividing the range given in the figure above by the density of the material. Let us now apply this procedure to determine the range of 300-keV beta particles in air. (Air has a density of 0.00129 g/cm3.) From the figure we see that a 300-keV electron has a range of 0.76 mm in a material with a density of 1 g/cm3. When this value is divided by the density of air, we find the range to be 59 cm. In general, the range of electron radiation in materials such as tissue is a fraction of a millimeter. This means that essentially all electron radiation energy is absorbed in the body very close to the site containing the radioactive material.
The effectiveness of a particular radiation in producing biological damage is often related to the LET of the radiation. The actual relationship of the efficiency in producing damage to LET values depends on the biological effect considered. For some effects, the efficiency increases with an increase in LET, for some it decreases, and for others it increases up to a point and then decreases with additional increases in LET. For a given biological effect, there is an LET value that produces an optimum energy concentration within the tissue. Radiation with lower LET values does not produce an adequate concentration of energy. Radiations with higher LET values tend to deposit more energy than is needed to produce the effect; this tends to waste energy and decrease efficiency.
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