Question

Physics in Modern Medicine

P5.1. Heavy metals such as lead (Z = 82) are excellent x-ray absorbers compared to water (composed of low Z oxygen (Z = 8) and hydrogen (Z = 1)). An average value of Z = 7.42 describes water-rich soft tissues in the body. For safety purposes it is often important to completely absorb x-rays in a protective layer, a process called shielding. Lead is often used to construct shields and protective garments, such as aprons, which prevent x-rays from hitting the entire body during localized procedures. Taking into account only differences in absorption due to differing values of Z, calculate how much more strongly an atom of lead absorbs x-rays by the photoelectric effect in comparison with a typical atom in soft tissue. (Here you are ignoring density. Since lead is denser than most materials in the body, this will lead to an even stronger relative absorption.)

Answer 1

Absorption coefficient, , which determines how strongly an atom absorbs X-rays if proportional to the fourth power of atomic number Z.

Therefore to determine how strongly an atom of lead (Z=82) absorbs X-rays in comparison with an atom of soft tissue (Z=7.42), we will compare their coefficients of absorption.

This means that due to differing values of only Z, absorption of x-rays by lead atom is 14915.6 times more than the absorption by soft tissues.