The amount of Carbon-14 left in the sample would be 35.85 atoms.
Data;
- Half-Life (T1/2) = 5730 years
- Initial Amount (No) = 200
- Time = 14,325 years
- Amount at time (t) = ?
What is Half-Life?
This is the time required for a radioactive substance to decay to half it's original size.
The half-life of a radioactive decay is given by
[tex]T_\frac{1}{2} = \frac{\ln2}{k}\\ k = \frac{In2}{T_\frac{1}{2} }\\ k = \frac{0.693}{5730} \\k = 0.000120[/tex]
k = disintegration constant
The amount present in a radioactive substance at time T is given by
[tex]N = N_oe^-^k^t\\[/tex]
Let's substitute the value and solve
[tex]N = 200 e^-^(^0^.^0^0^0^1^2^*^1^4^3^2^5^)\\N = 200e^-^1^.^7^1^9\\N = 35.85[/tex]
At the end of 14325 years, the amount of Carbon-14 left in the sample would be 35.85 atoms.
Learn more on radioactive decay here;
https://brainly.com/question/11152793
