Posted by **andrew** on Sunday, June 3, 2012 at 9:02pm.

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 -
**Elena**, Monday, June 4, 2012 at 11:06am
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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