Chapter 20, Problem 97RQ

Interpretation Introduction

Interpretation:

The concentration of calcium ions in the given sample of seawater is to be determined.

Concept Introduction:

For radioactive elements, the number of disintegrations per second occurring in them is defined as their 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 is follows as::

$\text{activity = k}N$

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

To calculate 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:

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