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A building has become accidentally contaminated with radioactivity. THe longest lived material in the building is strontium-90 (atomic mass of 90 Sr 38 is 89.9077). If the building initially contained 5.0kg of this subtstance and the safe level is less than 10.0 counts/min, how long will the building be unsafe?

You need to look up the half life of Sr-90 and also calculate the initial decay rate of 5.0 kg. The number or Sr-90 atoms initially is
(Avogadro's #)*(5000 g/89.9 moles/g) =
3.35*10^25 atoms.
The half life (from a handbook) is
T1/2 = 28 years = 8.84*10^8 s.
The decay constant is
lambda = 0.693/T1/2 = 7.84*10^-10 s^-1
The initial decay rate is therefore
(3.35*10^25) x (7.84*10^-10) =
2.6*10^16 counts/s
The time required for that to decay to 10 counts/s can be computed from the exponential decay law.
10 = 2.6*10^16 * e(-lambda*t)

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