Q. 5.68 - An Introduction to General, Organic, and Biological Chemistry

Question

The hall-life of oxygen- $15$ is $124 \mathrm{s}$. If a sample of oxygen- $15$ has an activity of $4000 \mathrm{Bq}$, hos many minutes will elapse before it has an activity of $5000 \mathrm{Bq}$ ? $(5,4)$

Step-by-Step Solution

Answer

It takes $6.2$  minutes to reach the activity of $500 Bq$

Step 1- Introduction

Half-life is the  time it takes for half of a given radioactive material to decay. The half-life of oxygen-$15$ is said to be $124$ seconds.

Step 2- Explanation (part a)

The activity of a given oxygen sample $15$ is $4000$ becquerels.

Becquerel is a unit of radioactivity. 

The symbol of Becquerel is $Bq$.

After a period of time, the activity of oxygen15 is $500 Bq$.

Step 3- Explanation (part b)

Calculate the number of half-lives to reach the activity of $500 Bq$, as shown below. 

$4000 \mathrm{Bq}\stackrel{\text{ thatfake }}{⟶}2000 \mathrm{Bq}\stackrel{\text{ 2hurfive }}{⟶}1000 \mathrm{Bq}\stackrel{\text{ 3hatflive }}{⟶}500 \mathrm{Bq}$

Therefore, three half-lives elapse before reaching the activity of $500 Bq$. The half-life is equivalent to $124 \$.$

Step 4- Explanation (part c)

Calculate the time required for the three half-lives and convert  to minutes, as shown below.

$3\text{ half-lives }=3\text{ hatf-tives }\times \frac{124,5}{1\text{ hatf-ife }}\times \frac{1 \min }{60 \mathrm{s}}$

$=6.2 \min$