Answer:
The decay takes 6min
Explanation:
The decay of an isotope as Thallium-208 follows the equation:
ln[A] = -kt + ln[A]₀
Where [A] is amount of isotope after time t
k is decay constant = ln 2 / t(1/2)
[A]₀ is initial amount of the isotope
Replacing:
[A] = 15.0g
k = ln 2 / t(1/2) = ln 2 / 3min = 0.23105 min⁻¹
t = ?
[A]₀ = 60.0g
ln[A] = -kt + ln[A]₀
ln[15.0g] = -0.23105 min⁻¹*t + ln[60.0g]
-1.38629 = -0.23105 min⁻¹*t
6min = t
The decay takes 6min
