Chapter 20, Problem 90RQ

Interpretation Introduction

Interpretation:

The activity of $\text{1}\text{.00 g}$ of ${}^{\text{90}}\text{Sr}$ in becquerels and in microcuries, is to be determined.

Concept Information:

Strontium-90 is produced by nuclear fission and a radioactive isotope of strontium. The strontium-90 undergoes β-decay with half-life of $28.79\text{ years}$. The number of disintegrations per second is the activity of a radioactive material whose SI unit is becquerel (Bq).

The number of radioactive $\text{nuclei }\left(\text{N}\right)$ is experimentally proportional to activity.

$\text{Activity}=\text{k}N$.

Here, $\text{k}$ is the decay constant that gives the activity per nuclide and $N$ is the number of nuclei.

The change in the number of nuclei per second is:

$\begin{array}{c}activity=\frac{\Delta N}{\Delta t}\\ =kN\end{array}$

Here, $\Delta t$ is the change in the time interval.

The above equation is called the law of radioactive decay which is a first-order kinetic process. The half-life of the first-order reaction is:

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

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

The relationship between the conversion of becquerel to curie is as:

$\text{1 Bq = }\left(\text{1 / 3}{\text{.7 × 10}}^{\text{10}}\right)\text{ Ci}$.

The relationship between the conversion of curies to microcuries is as:

$\text{ 1 Ci = 1000mCi, conversion fator is }\frac{\text{1000mCi}}{\text{1 Ci}}$