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andrew-mc [135]
3 years ago
14

When a living organism dies, it stops taking in new carbon. Thus, as the radioactive carbon-14 decays, the ratio of carbon-12 to

carbon-14 increases. The half-life of carbon-14 is 5,700 years. If you have a fossil that contains only 25% of the carbon-14 of a living organism, how old would you estimate this fossil would be?
Biology
1 answer:
Alexxandr [17]3 years ago
4 0

Answer: The fossil is 11459 years old.

Explanation:

Half-life of carbon-14 = 5700 years

First we have to calculate the rate constant, we use the formula :

k=\frac{0.693}{5700\text{years}}

k=1.21\times 10^{-4}\text{years}^{-1}

Now we have to calculate the age of the sample:

Expression for rate law for first order kinetics is given by:

t=\frac{2.303}{k}\log\frac{a}{a-x}

where,

k = rate constant  = 1.21\times 10^{-4}\text{years}^{-1}
t = age of sample  = ?
a = let initial amount of the reactant  = 100 g
x = amount decayed = 75 g
a - x = amount left after decay process  = 100 - 75 = 25 g  Now put all the given values in above equation, we get
[tex]t==\frac{2.303}{1.21\times 10^{-4}}\log\frac{100}{25}

t=11459years

The fossil is 11459 years old.

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