Question

A chest x ray uses 10 keV photons with an RBE of 0.85. A 60 kg person receives a 0.30 mSv dose from one chest x ray that exposes 25% of the patient’s body. How many x ray photons are absorbed in the patient’s body?

Short answer

Dose$=3.53x{10}^{-4}\raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$kg$}\right.$

$=1.6x{10}^{-15}J$

Step-by-step solution

Step 1{ Given Information

Then the dose is Given by

dose=

$$\begin{gathered} \left(\frac{doseequivalentinsv}{\left(RBE\right)}\right)Gy \\ =\left(\frac{0.30msv\left({\displaystyle \frac{{10}^{-3Sv}}{1msv}}\right)}{0.85}\right)Gy \\ =\left(\frac{0.30x{10}^{-3}sv}{0.85}\right)Gy \\ =3.53x{10}^{-4}Gy\left(\frac{1.00{\displaystyle \raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$kg$}\right.}}{1Gy}\right) \\ =3.53x{10}^{-4}\raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$kg$}\right. \end{gathered}$$

Calculation

The amount of energy received by the body is

$$\begin{gathered} E_{body}=\left(3.53x{10}^{-4}\raisebox{1ex}{$J$}\!\left/ \!\raisebox{-1ex}{$kg$}\right.\right)\left(25\%\right)\left(60kg\right) \\ =211.8x{10}^{-4}J\left(\frac{25}{100}\right) \\ =53x{10}^{-4}J \\ Theenergyofeachphotonis, \\ {E}_{photon=10keV} \\ =10keV\left(\frac{{10}^{3}ev}{1kev}\right) \\ ={10}^{4}ev\left(\frac{1.6x{10}^{-19}J}{1eV}\right) \\ =1.6x{10}^{-15}J \end{gathered}$$

Expression

photons absorbed patient's body=Therefore, the number of X-ray photons absorbed by the body is the ratio of the energy absorbed by the body and the energy absorbed by the photons

$$\begin{gathered} \frac{E_{body}}{E_{photon}} \\ =\frac{53x{10}^{-4}J}{1.6x{10}^{-15}J} \\ =3.31x{10}^{12} \end{gathered}$$