Chapter U1.15, Problem 11E

Interpretation Introduction

Interpretation:

Fraction of the original ₆C¹⁴present in a wooden axe handle needs to be calculated, if the age of the wooden axe handle is 17190 years old.

Concept introduction:

Carbon dating is a process by which age of an old wooden sample can be found out.

Decomposition of radioactive isotope of carbon, i.e., ₆C¹⁴ is a first order reaction from which the time required to disintegrate certain fraction of the original sample can be calculated. Half life is the time period in which half of the atoms in a sample is disintegrated. Half life of ₆C¹⁴ is 5700 years.

Answer to Problem 11E

Fraction of the original ₆C¹⁴present in 17190 years old wooden axe handle is 1/8.

Explanation of Solution

17190 year is approximatelty 3 half life for ₆C¹⁴.

As,

$17100=3\times 5700$

After each half life the sample remaining is ½.

Sample remaining after n^th half life is (1/2)n.

So after one half life remaining will be ½.

After 2 half life remaining will be ¼.

After 3 half life remaining will be 1/8.

Conclusion

Thus, the fraction of the original ₆C14 is 1/8 which will be in the 17900 years old wooden axe handle.