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The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only ​% of the​ carbon-14 expected in living​ matter, when did the tree​ die?.

Sagot :

The tree will die after 3480 years

Given: half-life of carbon-14 = 5600 years

percentage of carbon = 65%

To Find: when did the tree die

Solution:

T = half-life = 5600 years

I suppose you want the age of the charcoal in years.If 65% of the carbon 14 remains, then the amount left is 0.65 times the initial amount A0.

0.65A0 = A0(1/2)^t/T

0.65 = (0.5)^t/5600

ln(0.65) = (t/5600) ln(0.5)

t = 5600 ln(0.65) / ln(0.5) ≅ 3480 years

So, the tree will die after 3480 years

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