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 $5000\mathrm{Bq}$? $(5,4)$

Short answer

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

Step-by-step solution

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 islocalid="1652171100442" $500Bq$.

Step 3- Explanation (part b)

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

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

$=6.2\min$