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A building has become accidentally contaminated with radioactivity. The longest-lived material in the building is strontium-90. (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)

  • physics -

    Halflife for Sr-90
    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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