Chapter 24.2, Problem 9PP

Interpretation Introduction

Interpretation:

The amount of cobalt-60 left from 10 mg sample after one half life, two half lives and three half lives are 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 9PP

Amount remains in one half life, two half lives and three half lives are 5 mg, 2.5 mg and 1.25 mg.

Explanation of Solution

The amount of the sample is 10 mg. For the first half life, the amount remains is,

$\begin{array}{c}N\text{=}\text{10}\text{mg}{\left(\frac{\text{1}}{\text{2}}\right)}^{\text{1}}\\ \text{=5}\text{mg}\end{array}$

For the two half lives, the amount remains is,

$\begin{array}{c}N\text{=}\text{10}\text{mg}{\left(\frac{\text{1}}{\text{2}}\right)}^2\\ \text{=2}\text{.5}\text{mg}\end{array}$

For the three half lives, the amount remains is,

$\begin{array}{c}N\text{=}\text{10}\text{mg}{\left(\frac{\text{1}}{\text{2}}\right)}^3\\ \text{=1}\text{.25}\text{mg}\end{array}$

Conclusion

The measurement of radioactive decay is done in half lives.