Chapter 24.2, Problem 10PP

Interpretation Introduction

Interpretation:

The amount of strontium-90 present in the sample in the beginning 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 10PP

The amount of strontium-90 present in the sample in the beginning is 800 mg.

Explanation of Solution

The amount of strontium-90 remains (N) is $\text{25}\text{mg}$ and the half lives (n) are 5. All the values are to be put in the below equation.

$\begin{array}{c}N=N_0{\left(\frac{1}{2}\right)}^n\\ 25\text{mg}\text{=}{N}_0{\left(\frac{1}{2}\right)}^5\\ N_0=25\times 32\text{mg}\\ \text{=800}\text{mg}\end{array}$

So, the amount present in the beginning is 800 mg.

Conclusion

The measurement of radioactive decay is done in half lives.