Chapter 20, Problem 96RQ

Interpretation Introduction

Interpretation:

The activity of the sample Technetium-99m (gamma emitter, $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=6.02\text{ hr}$) at the end of the day, that is, after 8 hours is to be calculated given that it had an activity of $4.52\times {10}^{-6}\text{Ci}$ in early morning.

Concept Information:

Technetium-99m is the isotope of technetium that is a useful medical radioisotope. It is used as a radioactive tracer and also acts as gamma cameras. Its mass number is 99 and therefore it’s nucleus will last longer as it is in excited state.

The exponential form of the relation between concentration and time for a first-order reaction is as follows,

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

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

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