Question

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?

Answer 1

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.