Answer: The rock is 2000785 years old.
Explanation:
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
t = age of sample
a = initial amount of the reactant = 800
x = amount of daughter isotope = 600
a - x = amount left after decay process = amount of parent isotope = (800-600) = 200
Half life is the amount of time taken by a radioactive material to decay to half of its original value.
[tex]t_{\frac{1}{2}}=\frac{0.693}{k}[/tex]
[tex]k=\frac{0.693}{1000000}=0.000000693years^{-1}[/tex]
[tex]t=\frac{2.303}{0.000000693}\log\frac{800}{200}[/tex]
[tex]t=2000785years[/tex]
The rock is 2000785 years old.
