Chapter 24, Problem 80A

Interpretation Introduction

Interpretation:

The amount of sample remains after 90 minutes needs to be determined.

Concept introduction:

Half line is the time required for one-half of a radioisotope’s nuclei to decay into its products.

Answer to Problem 80A

Amount of sample remains out of 165g after 90 minutes have passed is 5.15g.

Explanation of Solution

Given information,

$\begin{array}{c}\text{Half}\text{life}\text{of}\text{Technetium-104=18}\text{minutes}\\ \text{Initial}\text{amount=165g}\\ \text{Time}\text{passed=90minutes}\end{array}$

Remaining amount of Radiation,

$\text{N}={\text{N}}_{\circ }{\left(\frac{1}{2}\right)}^{\text{n}}$

where ,

$\begin{array}{l}\text{N}=\text{remaining}\text{amount}\\ {\text{N}}_{\circ }=\text{initial}\text{amount}\\ \text{n}=\text{number}\text{of}\text{half}\text{lives}\end{array}$

Let us compare the time that has passed to the isotope’s half-life, it can be seen that 90 minutes is exactly 5 times of half-lives.

Therefore,

$\text{n}=\text{5}$

So, amount remaining

$\begin{array}{c}\text{N}={\text{N}}_{\circ }{\left(\frac{1}{2}\right)}^{\text{n}}\\ \text{N}=165{\left(\frac{1}{2}\right)}^5\\ \text{N}=\frac{\text{165}}{\text{35}}\\ \text{N}=\text{5}\text{.15625g}\end{array}$

Conclusion

To calculate number of half-lives, compare the half life time and the time passed.