Question

Carbon 14 (14C) dating assumes that the carbon dioxide on Earth today has the same radioactive content as it did centuries ago. If this is true, the amount of 14C absorbed by a tree that grew several centuries ago should be the same as the amount of 14C absorbed by a tree growing today. A piece of ancient charcoal contains only 19% as much radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal given that the half-life of 14C is 5700 years?

Answer 1

23388 years

Step-by-step explanation:

Now we have to use the formula;

0.693/t1/2 = 2.303/t log No/N

Where

t1/2 = half life of the C-14 = 5700

t= age of the sample

No= radioactive material in a modern sample = No

N= radioactive material in a sample being studied. = 0.81No( since the amount N= No-0.19No)

Hence;

0.693/5700 = 2.303/t log No/0.81No

0.693/5700 = 2.303/t log 1/0.81

0.693/5700 = 2.303/t × 1.235

0.693/5700= 2.844/t

1.216×10^-4= 2.844/t

t= 2.844/1.216×10^-4

t= 23388 years