Question 28.QE.12: Ionsproduced by a chest X-ray In a typical chest X-ray about......

Solve and evaluate     The RBE of X-rays is 1. Thus, the dose of X-rays in rem equals the absorbed dose in rad. For an absorbed dose of 10 mrad, we can insert the known values and solve the equation to determine the energy absorbed per kilogram of exposed tissue:

10 \mathrm{mrad}=\left(10 \times 10^{-3} \mathrm{rad}\right)\left(\frac{10^{-2} \mathrm{~J} / \mathrm{kg}}{1 \mathrm{rad}}\right)=10^{-4} \mathrm{~J} / \mathrm{kg}

Because 5 kg of tissue receives this dose, the total absorbed energy is

(5 \mathrm{~kg})\left(10^{-4} \mathrm{~J} / \mathrm{kg}\right)=5 \times 10^{-4} \mathrm{~J}

We can determine the number of X-ray photons by dividing this result by the energy of a single photon:

\frac{5 \times 10^{-4} \mathrm{~J}}{\left(50,000 \frac{\mathrm{eV}}{\text { photon }}\right)\left(\frac{1.6 \times 10^{-19} \mathrm{~J}}{\mathrm{eV}}\right)}=6 \times 10^{10} \text { photons }

or 60 billion photons. Because the energy of each photon is so large compared to the typical ionization energy of atoms and molecules, it’s reasonable to suggest that each photon will produce approximately 100 ions. Therefore, the number of ions is approximately

6 \times 10^{10} \text { photons } \times 100 \text { ions/photon }=6 \times 10^{12} \text { ions }

Try it yourself:    What number of ions may be produced by a bilateral mammogram, assuming that each breast has a mass of 0.5 kg, the absorbed dose for both breasts is 0.2 rad, and 50,000-eV X-ray photons are used?

Answer:  \approx 3 \times 10^{11} \text { photons or } 3 \times 10^{13}  if each photon causes 100 ions.