Measuring Radiation Dosage — Question 4

Question 4

Activity becomes dose only after emission and absorption are specified

A source has constant activity $\mathcal A=10^6\,\mathrm{Bq}$ during a 600 s interval. Each decay emits on average .500 photons of energy 1.00 MeV. A specified absorber of mass .100 kg retains .0100 of the total photon energy emitted. Use $1\,\mathrm{MeV}=1.60\times10^{-13}\,\mathrm J$.

1. Find the emitted photon number and absorbed energy.

2. Find absorbed dose and identify the factors that prevent activity alone from determining dose.

Question 4 - Solution

Activity becomes dose only after emission and absorption are specified

(a) Method and calculation

$$\boxed{N_\gamma=\mathcal A t y=(10^6)(600)(.500)=3.00\times10^8}.$$$$\boxed{E_{\mathrm{abs}}=fN_\gamma E_\gamma=.0100(3.00\times10^8)(1.60\times10^{-13})=4.80\times10^{-7}\,\mathrm J}.$$

(b) Interpretation and further calculation

$$\boxed{D=E_{\mathrm{abs}}/m=4.80\times10^{-6}\,\mathrm{Gy}=4.80\,\mu\mathrm{Gy}}.$$$$\boxed{D=\mathcal A t\,yE_\gamma f/m}\quad\text{requires yield, energy, deposition fraction and mass}.$$

Physical check

The deposition fraction already includes geometry and energy escape for the stated absorber. It must not be counted a second time as another efficiency.