Answer: The time required will be 19.18 years
Explanation:
All the radioactive reactions follows first order kinetics.
The equation used to calculate half life for first order kinetics:
[tex]k=\frac{0.693}{t_{1/2}}[/tex]
We are given:
[tex]t_{1/2}=4.7\times 10^1yrs[/tex]
Putting values in above equation, we get:
[tex]k=\frac{0.693}{4.7\times 10^1yr}=0.015yr^{-1}[/tex]
Rate law expression for first order kinetics is given by the equation:
[tex]k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}[/tex]
where,
k = rate constant = [tex]0.015yr^{-1}[/tex]
t = time taken for decay process = ?
[tex][A_o][/tex] = initial amount of the reactant = 2 g
[A] = amount left after decay process = (2 - 0.5) = 1.5 g
Putting values in above equation, we get:
[tex]0.015yr^{-1}=\frac{2.303}{t}\log\frac{2}{1.5}\\\\t=19.18yrs[/tex]
Hence, the time required will be 19.18 years
