24.137 CP - Chemistry: Molecular Nature Of Matter And Change

Question

At death, a nobleman in ancient Egypt was mummified and his body contained $\mathbf{1}\mathbf{.}\mathbf{4}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}\mathit{g}$of ${}^{\mathbf{40}}\mathit{K}\mathbf{ }\left(t_{1/2}=1.25\times {10}^9 yr\right)\mathbf{,}\mathbf{ }\mathbf{1}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{8}}\mathbf{ }\mathit{g}$ of ${}^{\mathbf{14}}\mathit{C}\mathbf{(}{\mathit{t}}_{\mathbf{1}\mathbf{/}\mathbf{2}}\mathbf{=}\mathbf{ }\mathbf{5730}\mathit{y}\mathit{r}\mathbf{)}$, and $\mathbf{4}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{14}}\mathit{g}$   of ${}^{\mathbf{3}}\mathit{H}\mathbf{(}{\mathit{t}}_{\mathbf{1}\mathbf{/}\mathbf{2}}\mathbf{=}\mathbf{12}\mathbf{.}\mathbf{26}\mathit{y}\mathit{r}\mathbf{)}$. Which nuclide would give the most accurate estimate of the mummy’s age? Explain

Step-by-Step Solution

Answer

Carbon-14 which has a half-life of 5730 years would be the best choice.

Step 1: Definition of half-life

Half-life in nuclear chemistry refers to the time that gets consumed when the substance’s concentration lowers to half or 50% of the concentration. It is represented as t_1/2.

Step 2: Explanation for the most accurate estimate of the mummy’s age.

The age of Egyptian mummies exists thousand years ago so the best choice is an isotope that has a half-life of a few thousand years ago. Carbon-14 is the nuclide that has a half-life of 5730 years, and it would be the best choice.