Respuesta :
Answer: 17 years
Explanation:
Expression for rate law for first order kinetics for radioactive substance is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant
t = age of sample
a = let initial amount of the reactant
a - x = amount left after decay process
a) for completion of half life:
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}{82years}=8.4\times 10^{-3}years^{-1}[/tex]
b) for 8900 g of the mass of the sample to reach 7700 grams
[tex]t=\frac{2.303}{8.4\times 10^{-3}}\log\frac{8900}{7700}[/tex]
[tex]t=17years[/tex]
Thus it will take 17 years
