A 75 kgperson receives a whole-body radiation dose of$\mathbf{2}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{}\mathbf{Gy}$, delivered by alpha particles for which thefactor is 12. Calculate (a) the absorbed energy in joules and the dose equivalent in (b) sieverts and (c) rem.

Mass of the person, m = 75 kg

Radiation or absorbed dose by the whole body, Asorbed dose =$2.4\times {10}^{-4}\mathrm{Gy}$

The value of RBE factor is 12.

The equivalent dose of radiation is a measure of the biological damage to the human body due to the ionizing radiation in the radioactive decay processes. The new international system (SI) unit of radiation dose, expressed as absorbed energy per unit mass of tissue is the SI unit "gray". 1 Gy = 1 Joule/kilogram or 1 Gy multiplied by RBE = 1 Sv or 1. RBE (relative biological effectiveness) is a relative measure of the damage done by a given type of radiation per unit of energy deposited in biological tissues.

Formulae:

The dose absorbed of a radiation source,

$\mathrm{Absorbed}\mathrm{dose}=\frac{\mathrm{Total}\mathrm{absorbed}\mathrm{energy}}{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{sample}}.......\left(1\right)$

The dose equivalent of a radiation source, $\mathrm{D}.\mathrm{E}=\mathrm{RBE}\times \mathrm{Absorbed}\mathrm{dose}.......\left(2\right)$

The conversion of sieverts into rem, $1\mathrm{Sv}={10}^2\mathrm{rem}.......\left(3\right)$

Using the given data in equation (1), we can get the energy absorbed by the whole body as follows:

$$\begin{gathered} \mathrm{E}=(2.4\times {10}^4\mathrm{Gy})\left(75\mathrm{kg}\right) \\ =18\mathrm{mJ} \end{gathered}$$

Hence, the value of absorbed energy is 18 mJ.

Using the above value in equation (2), we can get the dose equivalent of the radiation source in sieverts as follows:

$$\begin{gathered} \mathrm{D}.\mathrm{E}=12\times \left(2.4\times {10}^{-4}\mathrm{Gy}\right) \\ =2.9\times {10}^{-3}\mathrm{Sv} \end{gathered}$$

Hence, the value of dose equivalent is $2.9\times {10}^{-3}\mathrm{Sv}$.

From the above value in part (b) and the given concept, the value of dose equivalent in rem is given as:

$$\begin{gathered} \mathrm{D}.\mathrm{E}=2.9\times {10}^{-3}\left({10}^2\mathrm{rem}\right) \\ =0.29\mathrm{rem} \end{gathered}$$

Hence, the value of dose equivalent is 0.29 rem .