Question

Carbon-14 has a half-life of 5,730 years. If a sample contained 170. kg originally, how much isleft after 10,000. years?

Answer 1

Given that half life of the C14 is about 5730 years,

The rate constant is given as,

`\begin{gathered} \lambda=\frac{0.693}{\text{half life}} \\ =\frac{0.693}{5730\text{ years}} \\ =1.2*10^(-4)year^(-1) \end{gathered}`

Accorcting to law of radio active decay,

`N=N_0e^(-\lambda t)`

Substituing all known values,

`\begin{gathered} N=170\text{ kg}* e^{-(1.2*10^(-4)*10000)} \\ =170\text{ kg}*0.30 \\ =51\text{ kg} \end{gathered}`

Therefore, 51 kg of Carbon 14 will be left after 10000 years.