Respuesta :
Answer :
The amount after 1000 years will be, 4.43 grams.
The amount after 10000 years will be, 1.49 grams.
Step-by-step explanation :
Half-life = 5715 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}{5715\text{ years}}[/tex]
[tex]k=1.21\times 10^{-4}\text{ years}^{-1}[/tex]
Now we have to calculate the amount after 1000 years.
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]1.21\times 10^{-4}\text{ years}^{-1}[/tex]
t = time passed by the sample = 1000 years
a = initial amount of the reactant = 5 g
a - x = amount left after decay process = ?
Now put all the given values in above equation, we get
[tex]1000=\frac{2.303}{1.21\times 10^{-4}}\log\frac{5}{a-x}[/tex]
[tex]a-x=4.43g[/tex]
Thus, the amount after 1000 years will be, 4.43 grams.
Now we have to calculate the amount after 10000 years.
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]1.21\times 10^{-4}\text{ years}^{-1}[/tex]
t = time passed by the sample = 10000 years
a = initial amount of the reactant = 5 g
a - x = amount left after decay process = ?
Now put all the given values in above equation, we get
[tex]10000=\frac{2.303}{1.21\times 10^{-4}}\log\frac{5}{a-x}[/tex]
[tex]a-x=1.49g[/tex]
Thus, the amount after 10000 years will be, 1.49 grams.
