Chapter 31, Problem 48P

(a)

To determine

Comparison of the result to the normal allowed dose and estimation for a 50 kg adult.

Answer to Problem 48P

For a 50 kg adult, the estimated value of the allowed dose is $3\times {10}^{-4}\text{times}$

Explanation of Solution

Given:

Activity, $2000\text{ pCi}=\left(2000\times {10}^{-12}\right)\text{Ci/L}$

Milk drank per day, $\text{0}\text{.5 L}$

Energy released per day, $\text{1}\text{.5 MeV}$

Normal allowed dose per year, $\text{100 mrem}=100\text{ rad/Gy}$

Calculation:

Firstly, we need to convert the activity into dose per year as follows:

  $\begin{array}{l}=\left(\left(2000\times {10}^{-12}\right)\text{Ci/L}\right)\times \left(3.7\times {10}^{10}\text{decays/s/Ci}\right)\times \left(\frac{12}{3600}\text{s}\right)\times \left(0.5\text{L/day}\right)\\ =\left(1.598\times {10}^6\text{decay/day}\right)\times \left(0.15\times {10}^6\text{eV/decay}\right)\times \left(1.602\times {10}^{-19}\text{J/eV}\right)\times 365\\ =1.4\times {10}^{-5}\text{J/year}\end{array}$

For a 50 kg adult, the fraction of allowed dose can be given by:

  $\begin{array}{l}=\left(1.4\times {10}^{-5}\text{J/year}\right)\left(\frac{1}{50}\text{kg}\right)\\ =2.8\times {10}^{-7}\text{Gy/yr}\\ \text{=}\left(2.8\times {10}^{-7}\text{Gy/yr}\right)\left(100\text{ rad/Gy}\right)\\ =\left(2.8\times {10}^{-7}\text{Gy/yr}\right)\left(100\times {10}^{-3}\text{rem/yr}\right)\\ =3\times {10}^{-4}\text{times}\end{array}$

Conclusion:

For a 50 kg adult, the estimated value of the allowed dose is $3\times {10}^{-4}\text{times}$

(b)

To determine

Comparison of the result to the normal allowed dose and estimation for a 5 kg baby.

Answer to Problem 48P

For a 5 kg baby, the estimated value of the allowed dose is $3\times {10}^{-4}\text{times}$

Explanation of Solution

Given:

Activity, $2000\text{ pCi}=\left(2000\times {10}^{-12}\right)\text{Ci/L}$

Milk drank per day, $\text{0}\text{.5 L}$

Energy released per day, $\text{1}\text{.5 MeV}$

Normal allowed dose per year, $\text{100 mrem}=100\text{ rad/Gy}$

Calculation:

For a 5 kg baby, the estimated value can be calculated as follows:

  $\begin{array}{l}=\left(1.4\times {10}^{-5}\text{J/year}\right)\left(\frac{1}{5}\text{kg}\right)\\ =2.8\times {10}^{-6}\text{Gy/yr}\\ \text{=}\left(2.8\times {10}^{-6}\text{Gy/yr}\right)\left(100\text{ rad/Gy}\right)\\ =\left(2.8\times {10}^{-4}\text{Gy/yr}\right)\left(100\times {10}^{-3}\text{rem/yr}\right)\\ =3\times {10}^{-4}\text{times}\end{array}$

Conclusion:

For a 5 kg baby, the estimated value of the allowed dose is $3\times {10}^{-4}\text{times}$