Chapter 25, Problem 76A

Interpretation Introduction

Interpretation : The age of the object is to be calculated.

Concept Introduction : The phrase "radioactive decay" is used to describe the radioactivity occurrence. Radioactive elements are those elements or isotopes that release radiation and undergo radioactivity.

Answer to Problem 76A

The age of the object is $\text{11460}\text{years}$ .

Explanation of Solution

The carbon-14 content produces 4 counts per minute per gram of carbon.

The carbon-14 content that produces 16 counts per minute per gram of carbon.

The number of carbon-14 decayed is given as

  $\begin{array}{c}\text{Carbon}-14\text{decayed=}\frac{\text{4 }\cancel{\text{counts per minute per gram}}}{\text{16 }\cancel{\text{counts per minute per gram}}}\\ =\frac{1}{4}\\ ={\left(\frac{1}{2}\right)}^2\end{array}$

It is $2$ half-lives old.

One half-life is $5.73\times {10}^3\text{years}$ .

Two half-lives old is given as

  $2\times 5.73\times {10}^3\text{years}\text{=11460}\text{years}$

So, the age of the object is $\text{11460}\text{years}$ .