Chapter 24.2, Problem 16SSC

Interpretation Introduction

Interpretation:

The amount of 10.0 g of sample of americium-241 remains after four half lives needs to be calculated.

Concept introduction:

The time needed for one half of nuclei of radioisotope to decay into its products is the half life. The formula to calculate remaining amount of radioactive element is,

$N=N_0{\left(\frac{1}{2}\right)}^n$

Where $N$ is remaining amount, $N_0$ is the initial amount and n is the number of half lives that have passed.

Answer to Problem 16SSC

The amount of 10.0 g of sample of americium-241 remains after four half lives is 0.625 g.

Explanation of Solution

Amount of sample ( $N_0$ ) is 10 g and number of half lives (n) is 4.

$\begin{array}{c}N=N_0{\left(\frac{1}{2}\right)}^n\\ =10\times {\left(\frac{1}{2}\right)}^4\\ =0.625\text{g}\end{array}$

Conclusion

The measurement of radioactive decay is done in half lives.