Chapter 31, Problem 45P

To determine

To find:The dose rate over the whole body

Answer to Problem 45P

  $8.2\times {10}^{-7}\frac{\text{Gy}}{\text{ day }}$

Explanation of Solution

Given data:

Energy released by each gamma ray, $122\text{keV}/\mathrm{\gamma }$

Mass of person, $\mathrm{m}=70\text{kg}$

Deposited percentage is 50% = 0.5

Person swallowed $1.85\times {10}^{-6}\text{Ci}$ of $\text{C}\text{o}$

Calculation:

The dose rate over the whole body

  $\begin{array}{l}\left(1.85\times {10}^{-6}\text{Ci}\right)\left(3.70\times {10}^{10}\frac{\mathrm{\gamma }/\text{s}}{\text{Ci}}\right)\left(86,400\frac{\text{s}}{\text{day}}\right)(0.50)(122\text{keV}/\mathrm{\gamma })\left(1.60\times {10}^{-16}\text{J}/\text{keV}\right)\left(\frac{1}{70\text{kg}}\right)\\ =8.24\times {10}^{-7}\frac{\text{J}/\text{kg}}{\text{ day }}\\ \approx 8.2\times {10}^{-7}\frac{\text{Gy}}{\text{ day }}\end{array}$

Conclusion:

The dose rate over the whole bodyis $8.2\times {10}^{-7}\frac{\text{Gy}}{\text{ day }}$