Question

An organic sample of mass4.00 kg absorbs2.00Jvia slow neutron radiation (RBE=5). What is the dose equivalent (mSv)?

Short answer

The dose equivalent in mSv is 2.5 mSv.

Step-by-step solution

The given data

1. Mass of the sample, m = 400 kg
2. Energy absorbed by the sample, Q = 2. 00 mJ
3. Absorption of neutron radiation of the sample, RBE = 5

Understanding the concept of dose equivalent  

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 =1 Sv. 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,$\mathrm{Aborbed}\mathrm{dose}=\frac{\mathrm{Total}\mathrm{absorbed}\mathrm{energy}}{\mathrm{Mass}\mathrm{of}\mathrm{the}\mathrm{sample}}$ (1)

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

Calculation of the dose equivalent

Using the given data in equation (1), the absorbed dose of the radiation from the source can be given as follows:

$$\begin{gathered} \mathrm{Absorbed}\mathrm{dose}=\frac{2\times {10}^{-3}\mathrm{J}}{4\mathrm{kg}} \\ =5\times {10}^{-4}\mathrm{J}/\mathrm{kg} \\ =5\times {10}^{-4}\mathrm{Gy} \end{gathered}$$

Now, the dose equivalent of the radiation to the human body can be given using the above data in equation (2) as follows:

$$\begin{gathered} \mathrm{D}.\mathrm{E}=5\times (5\times {10}^{-4}\mathrm{Gy}) \\ =25\times {10}^{-4}\mathrm{Sv}\left(\frac{{10}^3\mathrm{mSv}}{1\mathrm{Sv}}\right) \\ =2.5\mathrm{mSv} \end{gathered}$$

Hence, the value of dose equivalent is 2.5 mSv.