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

Question

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.

Accepted Answer

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)

[latex]\mathrm{= 5.0 imes 10^{-4} J/kg.}[/latex]

The total energy absorbed is

[latex]\mathrm{(5.0 imes 10^{-4} J/kg)(5 kg) = 2.5 imes 10^{-3} J}[/latex]

[latex]\mathrm{= 1.56 imes 10^{16} eV.}[/latex]

The energy of one x-ray photon is [latex]\mathrm{50 keV = 5.0 imes 10^4 eV}.[/latex]

The number of x-ray photons is

[latex]\mathrm{\frac{1.56 imes 10^{16} eV}{5.0 imes 10^4 eV}=3.1 imes 10^{11} photons. } [/latex]

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 [latex]\mathrm{1.25 imes 10^ 4 J.}[/latex]

Practice Problem: In a diagnostic x-ray procedure, [latex]\mathrm{5.00 imes 10^{10} photons}[/latex] 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: [latex]\mathrm{4.97 imes 10^{-4} J, 0.0828 rem.}[/latex]

Question 30.5: Radiation exposure during an x ray In this example we will a...

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