Answer: The initial amount of Uranium-232 present is 11.3 grams.
Explanation:
All the radioactive reactions follows first order kinetics.
The equation used to calculate half life for first order kinetics:
\(t_{1/2}=\frac{0.693}{k}\)
We are given:
\(t_{1/2}=68.9yrs\)
Putting values in above equation, we get:
\(k=\frac{0.693}{68.9}=0.0101yr^{-1}\)
Rate law expression for first order kinetics is given by the equation:
\(k=\frac{2.303}{t}\log\frac{[A_o]}{[A]}\)
where,
k = rate constant = \(0.0101yr^{-1}\)
t = time taken for decay process = 206.7 yrs
\([A_o]\) = initial amount of the reactant = ?
[A] = amount left after decay process = 1.40 g
Putting values in above equation, we get:
\(0.0101yr^{-1}=\frac{2.303}{206.7yrs}\log\frac{[A_o]}{1.40}\)
\([A_o]=11.3g\)
Hence, the initial amount of Uranium-232 present is 11.3 grams.
