Answer :
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
Final answer:
Thallium-208 has a half-life of 3 minutes. It will take 30 minutes for 60.0 g of thallium-208 to decay to 15.0 g.
Explanation:
The half-life of Thallium-208 is 3 minutes, which means that in each 3-minute interval, half of the remaining thallium-208 will decay. To determine how long it will take for 60.0 g of thallium-208 to decay to 15.0 g, we can use the concept of half-life.
First, we need to determine how many half-lives it will take for the amount to decrease from 60.0 g to 15.0 g.
Since each half-life is 3 minutes, dividing the total time by the half-life will give us the number of half-lives: Number of half-lives = (total time) / (half-life) = (30 min) / (3 min) = 10 half-lives
So, it will take 10 half-lives, or 30 minutes for 60.0 g of thallium-208 to decay to 15.0 g.
Learn more about Half-life here:
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