Answer:
The age of the rock 10.00 million years old.
Explanation:
Half-life = 5 million years
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
[tex]k=\frac{0.693}{5\text{million years}}[/tex]
[tex]k=0.1386\text{million years}^{-1}[/tex]
Now we have to calculate the time passed.
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{N_o}{N}[/tex]
where,
k = rate constant = [tex]1.21\times 10^{-4}\text{ years}^{-1}[/tex]
t = time passed by the sample or age of the sample = ?
[tex]N_o[/tex] = let initial amount of the reactant = x
N= amount left after decay process = 25% of x =0.25 x
[tex]t=\frac{2.303}{0.1386\text{million years}^{-1}}\log\frac{x}{0.25}[/tex]
[tex]t=10.00 \text{million years}[/tex]
The age of the rock 10.00 million years old.
