Chapter 19, Problem 29A

Interpretation Introduction

Interpretation: The assumption made on carbon-14 in dating artifacts and the reason for the significance of the assumption has to be given.

Concept introduction: A process for dating ancient articles made from wood or cloth is called as radiocarbon dating (or) carbon-14 dating. Radiocarbon dating is based on $C$ that decays by production of $\beta \text{-}$ particle.

  $C\to e+N$

When neutrons of high energy from space collide with nitrogen-14, carbon-14 is produced in the atmosphere.

  $N+n\to C+H$

The half-life of $C$ is $\text{5,730}$ years.

Answer to Problem 29A

The amount of carbon-14 in the atmosphere is constant. The importance of the assumption is it tells about the balance between the amount produced and the amount it naturally decays.

Explanation of Solution

A process for dating ancient articles made from wood or cloth is called as radiocarbon dating (or) carbon-14 dating. The nuclide that is used in dating artifacts is carbon-14 $\left(\text{C}\right)\text{.}$

Radiocarbon dating is based on $C$ that decays by production of $\beta \text{-}$ particle.

  $C\to e+N$

When neutrons of high energy from space collide with nitrogen-14, carbon-14 is produced in the atmosphere.

  $N+n\to C+H$

The half-life of $C$ is $\text{5,730}$ years.

Carbon-14 could be used to date wood and cloth artifacts because carbon-14 along with other isotopes of carbons reacts with oxygen to form carbon dioxide.

The assumption on carbon-14 is that carbon-14 in the atmosphere has not changed over time; the biosphere has the equal overall concentration of radiocarbon as the atmosphere due to equilibrium.

The assumption on carbon-14 is important because there is balance between the amount produced and the amount that naturally decays.

Conclusion

The amount of carbon-14 in the atmosphere is constant. The importance of the assumption is it tells about the balance between the amount produced and the amount it naturally decays.