Question

Two students scouring an archaeological site found what appeared to be fossil remains. The specimen was found to have a ratio of 14C/12C 0.795 times that found in current living plants. What would be the estimated age of the fossil remains? The half-life for carbon -14 is 5720 years.

Answer 1

Answer on Question #55006 - Chemistry - Other

Question:

Two students scouring an archaeological site found what appeared to be fossil remains. The specimen was found to have a ratio of 14C/12C 0.795 times that found in current living plants. What would be the estimated age of the fossil remains? The half-life for carbon -14 is 5720 years.

Solution:

Radioactive decay of $^{14}\mathrm{C}$ is a first order reaction described by equation $N = N_{0} \exp(-kt)$. It can be transformed as following $\ln\left(\frac{N}{N_0}\right) = -kt$; $k = \frac{\ln 2}{t_{\frac{1}{2}}}$; $\ln\left(\frac{N}{N_0}\right) = -t * \ln 2 / t_{1/2}$

$$t = - \ln \left(\frac {N}{N _ {0}}\right) * \frac {t _ {\frac {1}{2}}}{\ln 2} = - \ln 0. 7 9 5 * 5 7 2 0 \ln 2 = 1 8 9 3 (y e a r s)$$

Answer:

The estimated age of the fossil remains is 1890 years

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