Solutions 7

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These exercises it might be usfull to have wallet cards they can for instance be found at Nudat 2

1:

1. It is in total 3.58 mol = 2.1562[math]\cdot[/math] 10²⁴ atoms of potassium in a average human where 12% that is 2.5876[math]\cdot[/math]10²⁰ is ⁴⁰K
   [math]T_{(1/2)}=1.28\cdot10^{9}=4.0283 \cdot 10^{16}\,s[/math]
   [math]\lambda= \frac{\ln 2}{T_{(1/2)}} = \frac{ln2}{4.0283\cdot 10^{16}}=1.7206\cdot 10^{-17}\, s^{-1}[/math]
   [math]D=\lambda \cdot N= 2.5876\cdot10^{20}\cdot 1.7206\cdot 10^{-17} s^{-1}=4452.45\, Bq[/math]
2. First calculate the dose per second:
   [math]4452.45\, Bq \cdot 400\, keV Bq^{-1} = 1.78\cdot 10^{6} keV s^-1[/math]
   Then calculate it to joule per second:
   [math]1.602\cdot 10^{-16}\, J/keV \cdot 1.78\cdot 10^{6}\, keV/s = 2.8534\cdot 10^{-10}\, J/s[/math]
   which gives:
   [math]2.8534\, J/s \cdot\frac{10^{-10}}{70\, kg} = 4.076\cdot 10^{-12} J/(kg s)[/math]
   As the dose can be assumed to be constant trough a human life for each year we will recive a dose of:
   [math]3.145\cdot 10^7 \, \frac{s}{year} \cdot 4.076\cdot 10^{-12}\, \frac{J}{kg\, s} = 1.28 10^{-4}\, \frac{Gy}{year} = 0.13\, \frac{mGy}{year}[/math]

2:

1. [math]\lambda = 7.3466 \cdot ^{-10}s^{-1}[/math]
   [math]D=\lambda \cdot N \rightarrow N=\frac{D}{\lambda}=\frac{6000 \, Bq}{\lambda}=8.17\cdot 10^{12}[/math]
   which is 1.36[math]\cdot[/math]10_-11 mol of ₁₃₇Cs
2. Calculate the initial dose rate from the renderer meat:
   [math]6000\, Bq \cdot 200 keV\cdot 1.6\cdot 10^{-16} \frac{J}{kev}=1.92\cdot 10^{-10}\frac{J}{s}[/math]
   for a person of 70 kg this gives a dose of 2.74[math]\cdot[/math]10^-12Gy/s.
   Then calculate the real half-life
   [math]T_{rel}=\frac{T_{B}\cdot T_{P}}{T_{B}+T{P}}\rightarrow \frac{0.302\cdot 30}{0.302+30}=108.9\, d[/math]
   Then the total dose will be:
   [math]D_{tot}=\int^{t=\infty}_{t=0}D_{0}\cdot e^{-\lambda t}dt=-\frac{D_{0}}{\lambda}\left[e^{-\lambda t}\right]^{t=\infty}_{t=0}=\frac{D_{0}}{\lambda}(0-1)[/math]
   [math]=\frac{2.74\cdot 10^{-12}}{7.367\cdot 10^{-8}}=0.580\, mGy/year[/math]

3:
ALI (Annual Limit of Intake) is the amount of activity in a certain material that when consumed gives a radiaton dose of 20 mSv. There is ALI-values for both inhalation and consummation of radioactivity material.

both chemical and physical properties makes a substance dangerous. Decay type, half-life and energy of radiation determine the dose received. The chemical form and the chemical properties of the material determine if it is accepted or if it gets enriched in the body. For instance a alpha-emitter can be inhaled and do a substantial amount of damage in the body. A combination of short physical and long biological half-life will cause a lot of a deposited into the body and the person will recive a large dose. Some example of interest is iodine, which is enriched in the thyroid gland. Polonium and a lot of other substances which gets enriched in the skeleton. Radon as a gas which often is found in cellars of houses on uranium rich ground.