physics
posted by andrew .
A building has become accidentally contaminated with radioactivity. The longestlived material in the building is strontium90. (The atomic mass of Sr is 89.9077 u.) If the building initially contained 4.8 kg of this substance and the safe level is less than 10.0 counts/min, how long will the building be unsafe? (in years)

Halflife for Sr90
T =28.79 yr
Decay constant
λ=ln2/T =0.693/28.79•365•24•3600 =
=7.63•10^10 s^1
Initial number of nuclei
Nₒ=m/mₒ=4.8/89.9077•1.66•10^27 = =3.2•10^25.
Initial activity
Aₒ = λ •Nₒ =7.63•10^10 • 3.2•10^25= =2.44•10^16 Bq.
A =10 counts/min =
=10/60 counts/s =0.167 Bq.
From the law of radioactive decay N=Nₒ•e^ λ•t
A=Aₒ•e^ λ•t,
A/Aₒ= e^ λ•t,
A/Aₒ=0.167/2.44•10^16=6.84•10^18
t =  ln(A/Aₒ)/λ = 39.5/7.63•10^10 =
=5.18•10^10 s =1643 years.
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