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2. Scientists find a piece of wood that is thought to be from an ancient fire circle. They find that the wood contains an amount of carbon-14 (14C) that is approximately 1/13 of the current atmospheric 14C levels. Using N(t)=N0*e(-lambda*t) determine how many years ago the tree was chopped down to be used for the firewood. If you started with 3 million carbon-14 atoms, how many atoms would remain in the wood? 14C has a t1/2 of 5,750 years; lambda = ln(2)/t1/2.

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Answer:

Explanation:1/2=5750 years,

1/2=5750 years, 1/2(1/2)=1/4, (1/2)(1/2)(1/2)=1/8, (1/2)(1/2)(1/2)(1/2)=1/6

4 half lives have passed so 4(5750)=23000 years since the tree was chopped down

1000000 atoms (1/2)=500000 atoms(1/2)=250000(1/2)=125000(1/2)=62500 atoms would remain in the wood after 4 half lives

Dinosaurs became extinct around 62 million years ago, so if 14C's half life has a value of 5750 years, it would be gone or in such small amounts that dating would be ineffective today.

As Potassium decays into Argon in 1.3 billion years, apart from volcanic activity, it would enable geologists to effectively date things that are really, really, really old.

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