Chapter 20, Problem 98RQ

Interpretation Introduction

Interpretation:

The concentration of calcium ions in a sample of milk is to be determined and whether the given sample meets the concentrations, stated on a milk carton or not is to be predicted.

Concept Introduction:

For radioactive elements, the number of disintegrations per second is defined as an activity. Mathematically, it is represented as follows:

$\begin{array}{c}1\text{Ci}=3.7\times {10}^{10}{\text{disintegrations s}}^{-1}\\ 3.7\times {10}^{10}{\text{disintegrations s}}^{-1}\text{= }3.7\times {10}^{10}\text{Bq}\end{array}$

The activity is known to be proportional to the number of radioactive nuclei, $N$ For a sample of radioactive material. The expression follows as:

$\text{activity = k}N$

Here, $\text{k}$ is the decay constant (constant of proportionality).

For the change in the number of nuclei per second:

$\begin{array}{c}\text{activity}=-\frac{\Delta N}{\Delta t}\\ =\text{k}N\end{array}$

The half-life for a first-order reaction is given as,

$t_{1/2}=\frac{\text{ln 2}}{k}$