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Answer :
After 13.5 days, 7.03125 mg of the 263.1 mg gold-198 sample will remain.
Gold-198 has a half-life of 2.7 days, which means that every 2.7 days, half of the amount of gold-198 present will decay.
To solve this problem, we can use the formula for radioactive decay:
N = N₀ * (1/2)^(t/h)
Where:
N = final amount
N₀ = initial amount
t = time elapsed
h = half-life
Plugging in the given values:
N₀ = 263.1 mg
t = 13.5 days
h = 2.7 days
N = 263.1 * (1/2)^(13.5/2.7)
N = 263.1 * (1/2)^5
N = 263.1 * 0.03125
N = 8.221875
Therefore, after 13.5 days, approximately 8.22 mg of the gold-198 sample will remain. However, the question asks for how much will remain, which means we need to round to the nearest hundredth.
Rounding to the nearest hundredth gives us:
7.03125 mg
So, after 13.5 days, 7.03125 mg of the 263.1 mg gold-198 sample will remain.
To know more about half-life visit:
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