physics
posted by soojung .
A building has become accidentally contaminated with radioactivity. THe longest lived material in the building is strontium90 (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 Sr90 and also calculate the initial decay rate of 5.0 kg. The number or Sr90 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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