Chapter 17, Problem 6SAQ

Interpretation Introduction

Interpretation: Calculate the amount of iron-59 left in the sample after $178\text{ days}$.

Concept Introduction: Half-life is the time taken by the quantity to reduce to its initial value. In other words, the time taken by the parent nuclides in radioactive decay is half to that of the daughter nuclides.

The total number of half-lives is calculated as:

$T=n\times t_{1/2}$

Here, T is the time required for decay, n is the number of half-lives and $t_{1/2}$ is the half-life.

The amount left in the sample is determined by:

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

Here, N is the amount of sample left after time T and $N_0$ is the initial amount of the sample.