Q24.61 P - Chemistry: Molecular Nature Of Matter And Change

Question

A  $\mathbf{\text{3.6}}$-kg laboratory animal receives a single dose of  data-custom-editor="chemistry" ${\mathbf{\text{8.92×10}}}^{\mathbf{\text{-4}}}$Gy. 

(a) How many rads did the animal receive?

 (b) How many joules did the animal absorb?

Step-by-Step Solution

Answer

$\begin{array}{l}\text{a.0.0892rad}\\ {\text{b.3.2112x10}}^{\text{-3}}\text{J}\end{array}$

Step 1: Gray and Rad

Gray is the metric unit and Rad is the CGS unit of radiation. The relation between them is as shown below:

1 Gy = 100 rd

 

Step 2: Explanation

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

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

To calculate the rads the animal receive, we just need to convert the given value to rads.

a. rads

 _{$\left({\text{8.92×10}}^{\text{-4}}\text{Gy}\right)\left(\frac{{\displaystyle \text{1rad}}}{{\displaystyle \text{0.01Gy}}}\right)\text{=0.0892rad}$}

b. Energy in Joules

 _{$\text{(0.0892rad)}\left(\frac{{\displaystyle \frac{{\displaystyle \text{0.01.J}}}{{\displaystyle \text{kg}}}}}{{\displaystyle \text{1rad}}}\right){\text{(3.6 kg)=3.2112×10}}^{\text{-3}}\text{ J}$}