Given that half life of the C14 is about 5730 years,
The rate constant is given as,
[tex]\begin{gathered} \lambda=\frac{0.693}{\text{half life}} \\ =\frac{0.693}{5730\text{ years}} \\ =1.2\times10^{-4}year^{-1} \end{gathered}[/tex]Accorcting to law of radio active decay,
[tex]N=N_0e^{-\lambda t}[/tex]Substituing all known values,
[tex]\begin{gathered} N=170\text{ kg}\times e^{-(1.2\times10^{-4}\times10000)} \\ =170\text{ kg}\times0.30 \\ =51\text{ kg} \end{gathered}[/tex]Therefore, 51 kg of Carbon 14 will be left after 10000 years.
