Question 30.5: Radiation exposure during an x ray In this example we will a...
Radiation exposure during an x ray
In this example we will apply the concept of biologically equivalent dose to a common medical x ray. During a diagnostic x ray, a broken leg with a mass of 5 kg receives an equivalent dose of 50 mrem. Determine the total energy absorbed and the number of x-ray photons absorbed if the x-ray energy is 50 keV.
SET UP We note that for x rays, RBE = 1, so the absorbed dose is equal to the equivalent dose. We express the absorbed dose in J/kg.
Find the energy of one x-ray photon, and then find the number of x-ray photons needed to supply the specified total energy.
SOLVE For x rays, RBE = 1, so the absorbed dose is
50 mrad = 0.050 rad = (0.050)(0.01 J/kg)
\mathrm{= 5.0 \times 10^{-4} J/kg.}
The total energy absorbed is
\mathrm{(5.0 \times 10^{-4} J/kg)(5 kg) = 2.5 \times 10^{-3} J}
\mathrm{= 1.56 \times 10^{16} eV.}
The energy of one x-ray photon is \mathrm{50 keV = 5.0 \times 10^4 eV}.
The number of x-ray photons is
\mathrm{\frac{1.56 \times 10^{16} eV}{5.0 \times 10^4 eV}=3.1 \times 10^{11} photons. }
REFLECT If the ionizing radiation had been a beam of alpha particles, for which RBE = 20, the absorbed dose needed for an equivalent dose of 50 mrem would be 2.5 mrad, corresponding to a total absorbed energy of \mathrm{1.25 \times 10^ 4 J.}
Practice Problem: In a diagnostic x-ray procedure, \mathrm{5.00 \times 10^{10} photons} are absorbed by tissue with a mass of 0.600 kg. The x-ray wavelength is 0.0200 nm. Find the total energy absorbed by the tissue and the equivalent dose in rem. Answers: \mathrm{4.97 \times 10^{-4} J, 0.0828 rem.}