Chapter 20, Problem 13STP

To determine

The amount of carbon-14 left after 17,190 years.

Answer to Problem 13STP

In a sample of 80 g of carbon-14, about 10 g of carbon-14 will be left after 17,190 years.

Explanation of Solution

Give info:

Amount of carbon-14 initially $=80\text{ g}$

Total number of years $=17,190\text{ years}$

Half-life of isotopes $=5,730\text{years}$

Formula used:

  $\mathrm{Number}ofhalf-lives=\frac{totalyears}{half-lifeofcarbon-14}$

Calculation:

  $\mathrm{Number}ofhalf-lives=\frac{17,190years}{5,730years}=3$

After each half-life the number of remaining undecayed nuclei decrease rapidly.

• After one half-life the number of remaining undecayed nuclei reduced to half.
• And after two half-lives the number of remaining undecayed nuclei reduced to one-fourth.
• And after 3 half-lives the number of remaining undecayed nuclei reduced to one-eighth that means out of 80 g only 10 g of carbon-14 remained.

Conclusion:

Thus,the amount of carbon-14 will left after 17,190 years if initially there is a sample of 80 g of carbon-14.