Chapter 19.1, Problem 5RQ

Interpretation Introduction

Interpretation: Reason as to why one-fourth of a given sample remains at the end of two half-lives is to be given.

Concept introduction: Half-life of a radioactive sample is the time taken by it to reduce its concentration to half. Formula used to calculate the amount of sample left after $n$ half-lives is

  $\text{Half-life}=\frac{1}{2^n}$

Answer to Problem 5RQ

After two half-lives, amount of sample left

  $\begin{array}{l}=\frac{1}{2^2}\\ =\frac{1}{4}\end{array}$

Explanation of Solution

Half-life of a radioactive sample is the time taken by it to reduce its concentration to half. After first half-life, the amount of radioactive sample reduces to half. After another half life, it further reduces to half making it one-fourth of the original sample amount.

Conclusion

As per the definition of half life, one-fourth of a given sample remains at the end of two half-lives.