Chapter 16, Problem 16.121P

Interpretation Introduction

Interpretation:

The fraction of radioactivity that remains after 30 days has to be calculated for the given sample.

Concept Introduction:

Radioactive decay follows first order kinetics.

For the first order reaction half-life equation can be written as follows,

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

Where $t_{1/2}$ is half-life period and $k$ is the rate constant.

For the first order reaction integrated rate equation can be written as follows,

$\ln {\left[A\right]}_t=\ln {\left[A\right]}_0-kt$

Where ${\left[A\right]}_t$ is the concentration of $A$ at time t, ${\left[A\right]}_0$ is the initial concentration of $A$ and $k$ is the rate constant.