Chapter 20, Problem 89RQ

Interpretation Introduction

Interpretation:

The activity of americium-241 (²⁴¹Am) in becquerels and in microcuries, is to be determined.

Concept Information:

The number of decays per second tells the activity of the radioactive material. Becquerels (Bq) is the SI unit of activity.

The number of radioactive nuclei (N) 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 grams to milligrams is as:

$\text{1 g = 1000 mg}$.

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:

${\text{1 Ci = 10}}^{\text{-6}}\text{Ci}$.

$\text{Since},\text{ 1 hr = 3600 s, hence, conversion factor is }\frac{\text{3600 s}}{\text{1 hr}}$

$\text{Since, 1 mol = 6}\text{.022}\times {\text{10}}^{\text{23}}\text{atoms, conversion cator is }\frac{\text{6}\text{.022}\times {\text{10}}^{\text{23}}\text{atoms }}{\text{1 mol }}$

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