Question

The measurement of radioactive decay can be useful tool in things such as Carbon-dating. For a carbon sample with mass 500kg and a half life of 5,730 years, calculate the remaining mass after 20,000years.

Answer 1

`\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &500\\ t=\textit{elapsed time}\dotfill &20000\\ h=\textit{half-life}\dotfill &5730 \end{cases} \\\\\\ A=500\left( (1)/(2) \right)^{(20000)/(5730)}\implies A\approx 0.00000001555302367~Kgs`