Chapter 24, Problem 24.97P

Interpretation Introduction

Interpretation:

Number of $Rads$ (Dose) received by $65\text{ kg}$ human each year has to be determined using the given data.

Concept Introduction:

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\ln \text{ 2}}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$

Decay rate can be calculated using the given equation as follows,

  $\begin{array}{c}\text{Deacy rate =kN}\\ \\ \text{where, }\\ \text{k = Deacy constant}\\ \text{N = No}\text{. of radioactive nuclei}\end{array}$

Mass of a substance can be determined from molar mass as given,

  $Mass\text{ = No}\text{. of moles}\times \text{Molar mass}$

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 $\text{gray }\left(Gy\right)\text{ and rad}.$

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

Unit conversion:

  $1\text{ MeV = }\left({\text{10}}^6\text{ eV}\right)\left(\frac{1.602\times {10}^{-19}\text{ J}}{1\text{ eV}}\right)$