Chapter 24, Problem 24.62P

(a)

Interpretation Introduction

Interpretation:

Number of $Gray$ (Dose) received by $70\text{ kg}$ person has to be determined using the given data.

Concept Introduction:

Radiation Dose is the dose quantity that explains the effects of ionizing radiation. It describes the quantity of radiation energy that is absorbed by a matter.

  $Dose\text{ = }\frac{Energy\left(Joules\right)}{Weight\left(kg\right)}$

The units commonly used to measure dose are $\text{gray }\left(Gy\right)\text{ and rad}.$

  $\begin{array}{l}\text{1 Gy = 1 J/kg}\\ \\ \text{1 rad = 0}\text{.01 J/kg = 0}\text{.01 Gy}\end{array}$

Explanation of Solution

Given information is shown below,

  $\begin{array}{c}No.\text{ of }{\beta }^{-}\text{ particle = 6}\text{.0}\times {\text{10}}^5\\ \\ Mass\text{ of person = 70 kg}\\ \\ \text{Energy of each }{\beta }^{-}\text{ particle = 8}\text{.74}\times {\text{10}}^{-14}\text{ J}\end{array}$

Energy absorbed is determined as follows,

  $\begin{array}{c}Energy\left(J\right)\text{}\text{ = }\left(\text{6}\text{.0}\times {\text{10}}^5{\beta }^{-}\right)\left(\text{8}\text{.74}\times {\text{10}}^{-14}\text{ J}/{\beta }^{-}\right)\\ \\ =\text{ 5}\text{.244}\times {\text{10}}^{-8}\text{ J}\end{array}$

Dose $\left(Gray\right)$ received by $95\text{ kg}$ human is calculated as given,

  $\begin{array}{c}Dose\text{ = }\left(\frac{\text{5}\text{.244}\times {\text{10}}^{-8}\text{ J}}{70\text{ kg}}\right)\left(\frac{1\text{ rad}}{\text{0}\text{.01 J/kg}}\right)\left(\frac{0.01\text{ Gy}}{1\text{ rad}}\right)\\ \\ =7.49\times {10}^{-10}\text{ Gy}\end{array}$

Dose $\left(Gray\right)$ received by $70\text{ kg}$ human is $7.49\times 10^{-10}Gy.$

(b)

Interpretation Introduction

Interpretation:

Number of $mrem$ received by $70\text{ kg}$ person has to be determined using the given data.

Concept Introduction:

Radiation Dose is the dose quantity that explains the effects of ionizing radiation. It describes the quantity of radiation energy that is absorbed by a matter.

The units commonly used to measure dose are $\text{gray }\left(Gy\right)\text{ and rad}.$

  $\begin{array}{l}\text{1 Gy = 1 J/kg}\\ \\ \text{1 rad = 0}\text{.01 J/kg = 0}\text{.01 Gy}\end{array}$

The tissue damage caused by the radiation depends on the exposure time, strength of the radiation and tissue type. Tissue damage can be determined by multiplying dose that is absorbed with RBE (Relative Biological Effectiveness).

The two units used to measure amount of damaged tissue in a person is $rem\left(\text{Roentgen Equivalent for Man}\right)$ and $\text{sievert}\left(Sv.\right)$

  $\begin{array}{l}No.\text{ of rem = no}\text{. of rads}\times \text{RBE}\\ \\ \text{1 Sv = 100 rem}\end{array}$

Explanation of Solution

Given information is shown below,

  $\begin{array}{c}No.\text{ of }{\beta }^{-}\text{ particle = 6}\text{.0}\times {\text{10}}^5\\ \\ Mass\text{ of person = 70 kg}\\ \\ \text{Energy of each }{\beta }^{-}\text{ particle = 8}\text{.74}\times {\text{10}}^{-14}\text{ J}\\ \\ \text{RBE = 1}\text{.0}\end{array}$

Energy absorbed is determined as follows,

  $\begin{array}{c}Energy\left(J\right)\text{}\text{ = }\left(\text{6}\text{.0}\times {\text{10}}^5{\beta }^{-}\right)\left(\text{8}\text{.74}\times {\text{10}}^{-14}\text{ J}/{\beta }^{-}\right)\\ \\ =\text{ 5}\text{.244}\times {\text{10}}^{-8}\text{ J}\end{array}$

Dose $\left(rad\right)$ received is calculated as given,

  $\begin{array}{c}Dose\text{ = }\left(\frac{\text{5}\text{.244}\times {\text{10}}^{-8}\text{ J}}{70\text{ kg}}\right)\left(\frac{1\text{ rad}}{\text{0}\text{.01 J/kg}}\right)\\ \\ =7.49\times {10}^{-8}\text{ rad}\end{array}$

Dose $\left(rad\right)$ received by $70\text{ kg}$ human is $7.49\times {10}^{-8}\text{ rad}$.

Number of $mrem$ received by $70\text{ kg}$ person is determined as shown below,

  $\begin{array}{c}No.\text{ of rem = no}\text{. of rads}\times \text{RBE}\\ \\ =\left(7.49\times {10}^{-8}\text{ rad}\right)\left(1.0\right)\left(\frac{1\text{ mrem}}{{10}^{-3}\text{ rem}}\right)\\ \\ =7.49\times {10}^{-5}mrem\end{array}$

Number of $mrem$ received by $70\text{ kg}$ person is $7.49\times {10}^{-5}mrem.$

(c)

Interpretation Introduction

Interpretation:

Number of $\text{sieverts }\left(Sv\right)$ received by $70\text{ kg}$ person has to be determined using the given data.

Concept Introduction:

Radiation Dose is the dose quantity that explains the effects of ionizing radiation. It describes the quantity of radiation energy that is absorbed by a matter.

The units commonly used to measure dose are $\text{gray }\left(Gy\right)\text{ and rad}.$

  $\begin{array}{l}\text{1 Gy = 1 J/kg}\\ \\ \text{1 rad = 0}\text{.01 J/kg = 0}\text{.01 Gy}\end{array}$

The tissue damage caused by the radiation depends on the exposure time, strength of the radiation and tissue type. Tissue damage can be determined by multiplying dose that is absorbed with RBE (Relative Biological Effectiveness).

The two units used to measure amount of damaged tissue in a person is $rem\left(\text{Roentgen Equivalent for Man}\right)$ and $\text{sievert}\left(Sv.\right)$

  $\begin{array}{l}No.\text{ of rem = no}\text{. of rads}\times \text{RBE}\\ \\ \text{1 Sv = 100 rem}\end{array}$

Explanation of Solution

Given information is shown below,

  $\begin{array}{c}No.\text{ of }{\beta }^{-}\text{ particle = 6}\text{.0}\times {\text{10}}^5\\ \\ Mass\text{ of person = 70 kg}\\ \\ \text{Energy of each }{\beta }^{-}\text{ particle = 8}\text{.74}\times {\text{10}}^{-14}\text{ J}\\ \\ \text{RBE = 1}\text{.0}\end{array}$

Energy absorbed is determined as follows,

  $\begin{array}{c}Energy\left(J\right)\text{}\text{ = }\left(\text{6}\text{.0}\times {\text{10}}^5{\beta }^{-}\right)\left(\text{8}\text{.74}\times {\text{10}}^{-14}\text{ J}/{\beta }^{-}\right)\\ \\ =\text{ 5}\text{.244}\times {\text{10}}^{-8}\text{ J}\end{array}$

Dose $\left(rad\right)$ received is calculated as given,

  $\begin{array}{c}Dose\text{ = }\left(\frac{\text{5}\text{.244}\times {\text{10}}^{-8}\text{ J}}{70\text{ kg}}\right)\left(\frac{1\text{ rad}}{\text{0}\text{.01 J/kg}}\right)\\ \\ =7.49\times {10}^{-8}\text{ rad}\end{array}$

Dose $\left(rad\right)$ received is $7.49\times {10}^{-8}\text{ rad}$.

Number of $Sv$ received by $70\text{ kg}$ person is determined as shown below,

  $\begin{array}{c}No.\text{ of rem = no}\text{. of rads}\times \text{RBE}\\ \\ =\left(7.49\times {10}^{-8}\text{ rad}\right)\left(1.0\right)\\ \\ =7.49\times {10}^{-8}rem\\ \\ No.\text{ of Sv = }7.49\times {10}^{-8}rem\left(\frac{0.01\text{ Sv}}{1\text{ rem}}\right)\\ \\ =7.49\times {10}^{-10}Sv\end{array}$

Number of $Sv$ received by $70\text{ kg}$ person is $7.49\times {10}^{-10}Sv.$