Respuesta :
Answer : The time passed in years is 20.7 years.
Explanation :
Half-life = 28.1 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}{28.1\text{ years}}[/tex]
[tex]k=2.47\times 10^{-2}\text{ 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{a}{a-x}[/tex]
where,
k = rate constant = [tex]2.47\times 10^{-2}\text{ years}^{-1}[/tex]
t = time passed by the sample = ?
a = initial amount of the reactant = 1.00 g
a - x = amount left after decay process = 0.600 g
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{2.47\times 10^{-2}}\log\frac{1.00}{0.600}[/tex]
[tex]t=20.7\text{ years}[/tex]
Therefore, the time passed in years is 20.7 years.
