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,
After each half life the sample remaining is ½.
Sample remaining after nth 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.
Thus, the fraction of the original 6C14 is 1/8 which will be in the 17900 years old wooden axe handle.
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