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Mkey [24]
3 years ago
15

Carbon-14 (14C) dating assumes that the carbon dioxide on the Earth today has the same radioactive content as it did centuries a

go. If this is true, then 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 similar tree today. A piece of ancient charcoal contains only 13% as much of the radioactive carbon as a piece of modern charcoal. How long ago was the tree burned to make the ancient charcoal? (The half-life of 14C is 5715 years. Round your answer to one decimal place.)
Chemistry
1 answer:
Nataly [62]3 years ago
8 0

<u>Answer:</u> The tree was burned 16846.4 years ago to make the ancient charcoal

<u>Explanation:</u>

The equation used to calculate rate constant from given half life for first order kinetics:

t_{1/2}=\frac{0.693}{k}

where,

t_{1/2} = half life of the reaction = 5715 years

Putting values in above equation, we get:

k=\frac{0.693}{5715yrs}=1.21\times 10^{-4}yrs^{-1}

Rate law expression for first order kinetics is given by the equation:

k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}

where,

k = rate constant  = 1.21\times 10^{-4}yr^{-1}

t = time taken for decay process = ? yr

[A_o] = initial amount of the sample = 100 grams

[A] = amount left after decay process =  13 grams

Putting values in above equation, we get:

1.21\times 10^{-4}=\frac{2.303}{t}\log\frac{100}{13}\\\\t=16864.4yrs

Hence, the tree was burned 16846.4 years ago to make the ancient charcoal

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