Chapter 20, Problem 95RQ

Interpretation Introduction

Interpretation:

The activity of radio-labeled sodium iodide sample made from Iodine-131 at the time of accidental exposure, in the unit $\text{Ci}/\text{g}$, is to be calculated when its activity after 28 days is $25.6\times {10}^{-5}\text{ Ci/g}$.

Concept Information:

The isotope of iodine is iodine-131 that emits radiation. This isotope is used in medicinal purposes as the bloodstream absorbs it in the gastrointestinal tract, gets concentrated in the thyroid gland and gland’s cell are destroyed by it.

The relation between concentration and time in exponential form for a first-order reaction is given by the following equation:

$\left[\text{A}\right]\text{=}{\left[\text{A}\right]}_{\text{0}}{e}^{-\text{k}t}$

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

$\begin{array}{c}{t}_{1/2}=\frac{\ln 2}{\text{k}}\\ =\frac{0.693}{\text{k}}\end{array}$