Chapter 24, Problem 24.103P

Interpretation Introduction

Interpretation:

Number of $Curies\text{ and becquerels}$ (Dose) produced by $1.0{\text{ mol }}^{40}K$ has to be determined.

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,

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

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:

  $\begin{array}{c}\text{1 Ci = 3}{\text{.70×10}}^{\text{10}}\text{ disintegrations per second}\left(dps\right)\\ \\ \text{1 Bq = 1dps}\end{array}$