Respuesta :
Answer : The correct option is, (A) The rock reached its closure temperature 6,400 years ago.
Explanation :
Half-life = 1600 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}{1600\text{ years}}[/tex]
[tex]k=4.33\times 10^{-4}\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]4.33\times 10^{-4}\text{ years}^{-1}[/tex]
t = time passed by the sample = ?
a = initial amount of the reactant = 6 g
a - x = amount left after decay process = 0.375 g
Now put all the given values in above equation, we get
[tex]t=\frac{2.303}{4.33\times 10^{-4}}\log\frac{6}{0.375}[/tex]
[tex]t=6404.36\text{ years}\approx 6400\text{ years}[/tex]
Therefore, the correct option is, (A) The rock reached its closure temperature 6,400 years ago.
