Q24.62 P - Chemistry: Molecular Nature Of Matter And Change

Question

A  $\text{70}$.-kg person exposed to $\text{90}$ Sr absorbs  ${\mathbf{\text{6x10}}}^{\mathbf{\text{5}}}\mathbf{\text{β}}$particles, each with an nergy of ${\mathbf{\text{8.74x10}}}^{\mathbf{\text{-14}}}$ J. 

(a) How many grays does the person receive? 

(b) If the RBE is $\mathbf{\text{1.0}}$ , how many millirems is this? 

(c) What is the equivalent dose in sieverts (Sv)?

Step-by-Step Solution

Answer

$\begin{array}{l}{\text{a.7.4914x10}}^{\text{-10}}\text{Gy}\\ {\text{b.7.4914x10}}^{\text{-5}}\text{mrem}\\ {\text{c.7.4914x10}}^{\text{-10}}\text{Sv}\end{array}$

Step 1: Introduction

The SI unit of such energy absorption is the gray (Gy) which is equal to $\text{1}\frac{\text{J}}{\text{kg}}$ of body tissue. A more widely used unit is the rad (radiation-absorbed dose), which is one-hundredth as much:

 _{$\text{1rad=}\frac{\text{0.01.J}}{\text{kg}}\text{=0.01 Gy}$}

To find millirems, we need to convert  Gy to rads. Also, in order to find rems, we must multiply rads by the given RBE. Then we just have to convert rems to mrem.

To convert the dose to sieverts, we need to note that,

 _{$\text{1rem=0.01Sv}$}

Step 2: Calculation

a. Absorbed Energy (J)

 _{$\begin{array}{l}\left({\text{6x10}}^{\text{5}}\text{β}\right)\left({\text{8.74x10}}^{\text{-14}}\frac{\text{J}}{\text{β}}\right){\text{=5.244×10}}^{\text{-8}}\text{J}\frac{{\text{5.244x10}}^{\text{-8}}\text{.J}}{\text{70kg}}\left(\frac{\text{1rad}}{\frac{\text{0.01,J}}{\text{ kg}}}\right)\left(\frac{\text{0.01Gy}}{\text{1rad}}\right)\\ {\text{ =7.4914×10}}^{\text{-10}}\text{ Gy}\end{array}$}

b. mrem

Remember that the given RBE is 1 .

Therefore,

_{${\text{7.4914x10}}^{\text{-10}}\text{ Gy}\left(\frac{{\displaystyle \text{1rad}}}{{\displaystyle \text{0.01Gy}}}\right)\text{(1)}\left(\frac{{\displaystyle \text{1mrem}}}{{\displaystyle {\text{10}}^{\text{-3}}\text{rem}}}\right){\text{=7.4914x10}}^{\text{-5}}\text{mrem}$} 

c. Dose (Sv)

 _{${\text{7.4914x10}}^{\text{-5}}\text{ mrem }\left(\frac{{\displaystyle {\text{10}}^{\text{-3}}}}{{\displaystyle \text{1mrem}}}\right)\left(\frac{{\displaystyle \text{0.01Sv}}}{{\displaystyle \text{1rem}}}\right){\text{=7.4914x10}}^{\text{-10}}\text{ Sv}$}