Given:
The half-life of carbon-14 is 5730 years.
The initial amount of carbon is I = 50 grams.
Explanation:
To find the final amount of carbon after 1000 years.
The fundamental decay equation is,
[tex]\begin{gathered} F=Ie^{-\lambda t} \\ \text{Where, }\lambda=\frac{\ln 2}{t_{\frac{1}{2}}} \end{gathered}[/tex]Let us find the radioactive constant first.
[tex]\begin{gathered} \lambda=\frac{\ln 2}{5730} \\ \lambda=0.00012096809 \end{gathered}[/tex]Then, the final amount of the corban-14 is,
[tex]\begin{gathered} F=50e^{-0.000121(1000)}^{} \\ =44.30g \end{gathered}[/tex]Hence, the amount of a 50-gram sample of Carbon-14 will be left in 1000 years is 44.30 g.
