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 :
[tex]k=\frac{0.693}{5700\text{years}}[/tex]
[tex]k=1.21\times 10^{-4}\text{years}^{-1}[/tex]
Now we have to calculate the age of the sample:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]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}[/tex]
[tex]t=11459years[/tex]
The fossil is 11459 years old.
