Chapter 7.5, Problem 36PPE

To determine

Amount of Carbon-14 left in a sample after 5000 years.

Answer to Problem 36PPE

  $3.8\times {10}^{-12}grams$ of Carbon-14 left in a sample after 5000 years.

Explanation of Solution

Given data:

Original contained carbon-14 is $7\times {10}^{-12}grams$

Formula used:

  $A=A_0{(2.7)}^{-\frac{3}{5}}$

Calculation:

So the original contained carbon-14 is $7\times {10}^{-12}grams$

  $\begin{array}{l}$ A=A_0{(2.7)}^{-\frac{3}{5}}$A_0=7\times {10}^{-12}\\ $ A=7\times {10}^{-12}{(2.7)}^{-\frac{3}{5}}$$ A=7\times {10}^{-12}{(19.7)}^{-\frac{1}{5}}$A=\frac{7\times {10}^{-12}}{1.8}\\ A=3.8\times {10}^{-12}grams\end{array}$

Conclusion:

  $3.8\times {10}^{-12}grams$ of Carbon-14 left in a sample after 5000 years.