Q24.60 P - Chemistry: Molecular Nature Of Matter And Change

Question

A  $\mathbf{\text{135}}$-lb person absorbs  ${\mathbf{\text{3.3×10}}}^{\mathbf{\text{-7}}}\mathbf{\text{ J}}$of energy from radioactive emissions. 

(a) How many rads does she receive? 

(b) How many grays (Gy) does she receive? 

 

Step-by-Step Solution

Answer

$\begin{array}{l}{\text{a)5.39×10}}^{\text{-7}}\text{rad}\\ {\text{b)5.39×10}}^{\text{-9}}\text{ Gy}\end{array}$

Step 1: The given data

-  _{$\text{1rad=0.01 J/kg=0.01 Gy}$}

- The mass of a person is  _{$135\text{lb}$}

- Person absorbs  _{$3.3\times {10}^{-7} \text{J}$}of energy from radioactive emissions

Step 2: Subpart (a)

The number of rads

Since 1 rad is$0.01 \text{J}/\text{kg}$  , first, we have to convert the mass of a person, from lb to  _$\text{kg}$

_{$\begin{array}{c}\text{ mass of a person }=135\text{lb}\times \frac{0.453592 \text{kg}}{1\text{lb}}\\ =61.235 \text{kg}\end{array}$}

So, the number of rads that a person received is

 

 $\begin{array}{c}\text{ Number of rad =}\frac{{\text{3.3×10}}^{\text{-7}}\text{ J}}{\text{61.235 kg}}\text{×}\frac{\text{1rad}}{\text{0.01 J/kg}}\\ {\text{ =5.39×10}}^{\text{-7}}\text{rad}\end{array}$

Step 3: Subpart (b)

The number of grays

 $\begin{array}{c}{\text{Number of grays =5.39×10}}^{\text{-7}}\text{rad×}\frac{\text{0.01 Gy}}{\text{1rad}}\\ {\text{ =5.39×10}}^{\text{-9}}\text{ Gy}\end{array}$