Respuesta :
Answer: [tex]3.80\times 10^9years[/tex]
Explanation:
Half-life of uranium = [tex]4.47\times 10^9[/tex] years
First we have to calculate the rate constant, we use the formula :
[tex]k=\frac{0.693}{4.47\times 10^9\text{years}}[/tex]
[tex]k=0.155\times 10^{-9}\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]0.155\times 10^{-9}\text{years}^{-1}[/tex]
t = age of sample = ?
a = let initial amount of the reactant = 100
a - x = amount left after decay process = [tex]\frac{55.5}{100}\times 100=55.5[/tex]
Now put all the given values in above equation, we get
[tex]t==\frac{2.303}{0.155\times 10^{-9}}\log\frac{100}{55.5}[/tex]
[tex]t=3.80\times 10^9years[/tex]
Thus the age of a rock specimen that contains 55.5% of its original number of atoms is [tex]3.80\times 10^9years[/tex]
