Chapter 16, Problem 15RQ

To determine

The reason for the carbon-14 dating not accurate for estimating the age of materials more than 50000 years old.

Answer to Problem 15RQ

The only trace amount of carbon-14 would be left after $50000\text{ years}$ , which is very small to be numerically accurate.

Explanation of Solution

The half-life of the carbon-14 is $5730$, which is a radioactive isotope of the carbon, which means that half of the carbon-14 atoms present in any plant or any body will be decay after the next $5730\text{years}$ and so forth. This method is used by the archeologists to estimate the age of the samples.

The radioactive decay rate is the numerical average of a large number of decaying atoms and the short life of the carbon-14 would be left after the 50000 years, which is too small to be accurate numerically.

Conclusion:

Therefore, the only trace amount of carbon-14 would be left after $50000\text{ years}$, which is very small to be numerically accurate.