Chapter 24, Problem 24.104P

(a)

Interpretation Introduction

Interpretation:

Fraction of Carbon-14 in a piece of charcoal after $\text{10}\text{.0 yr}$ has to be determined.

Concept Introduction:

Half-life: The time required for the concentration of a reactant to decrease to one half of its initial value.

  Thus, ${\text{[R]}}_{\text{t}}\text{=}\frac{{\text{[R]}}_{\text{0}}}{\text{2}}.$

Fraction of remaining radioactive isotope is given,

  $Fraction\text{ = }{\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$t_{1/2}$}\right.}$

(b)

Interpretation Introduction

Interpretation:

Fraction of Carbon-14 in a piece of charcoal after $\text{10}\text{.0}\times {\text{10}}^3\text{ yr}$ has to be determined.

Concept Introduction:

Half-life: The time required for the concentration of a reactant to decrease to one half of its initial value.

  Thus, ${\text{[R]}}_{\text{t}}\text{=}\frac{{\text{[R]}}_{\text{0}}}{\text{2}}.$

Fraction of remaining radioactive isotope is given,

  $Fraction\text{ = }{\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$t_{1/2}$}\right.}$

(c)

Interpretation Introduction

Interpretation:

Fraction of Carbon-14 in a piece of charcoal after $\text{10}\text{.0}\times {\text{10}}^4\text{ yr}$ has to be determined.

Concept Introduction:

Half-life: The time required for the concentration of a reactant to decrease to one half of its initial value.

  Thus, ${\text{[R]}}_{\text{t}}\text{=}\frac{{\text{[R]}}_{\text{0}}}{\text{2}}.$

Fraction of remaining radioactive isotope is given,

  $Fraction\text{ = }{\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$t_{1/2}$}\right.}$

(d)

Interpretation Introduction

Interpretation:

Reason for why radiocarbon dating more reliable for the fraction remaining after $\text{10}\text{.0}\times {\text{10}}^3\text{ yr}$ than that after $\text{10}\text{.0 yr}$ or after $\text{10}\text{.0}\times {\text{10}}^4\text{ yr}$ has to be determined.

Concept Introduction:

Half-life: The time required for the concentration of a reactant to decrease to one half of its initial value.

  Thus, ${\text{[R]}}_{\text{t}}\text{=}\frac{{\text{[R]}}_{\text{0}}}{\text{2}}.$

Fraction of remaining radioactive isotope is given,

  $Fraction\text{ = }{\left(\frac{1}{2}\right)}^{\raisebox{1ex}{$t$}\!\left/ \!\raisebox{-1ex}{$t_{1/2}$}\right.}$