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Strontium 90 (sr-90, a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. it is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. its half-life is 27 years. if the amount of sr-90 in a certain area is found to be four times the "safe" level, find how much time must elapse before the safe level is reached.

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"81 years" would be the time must elapse before the safe level is reached.

According to the question,

  • [tex]N(t) = \frac{N_0}{8}[/tex]
  •     [tex]T = 27 \ years[/tex]

The formula for the radioactive decay will be:

→ [tex]N(t) = N_0 e^{-\frac{ln \ 2}{T}t }[/tex]

By substituting the values, we get

→    [tex]\frac{N_0}{8} = N_0 e^{-\frac{ln \ 2}{27}r }[/tex]

→      [tex]\frac{1}{8} = e^{ln \ 2^{\frac{-t}{27} }}[/tex]

→      [tex]\frac{1}{8} = 2^{-\frac{t}{27} }[/tex]

→  [tex](\frac{1}{2} )^3 = (\frac{1}{27} )^{\frac{t}{27} }[/tex]

→       [tex]3 = \frac{t}{27}[/tex]

→       [tex]t = 81 \ years[/tex]

Thus the above approach is right.  

Learn more:

https://brainly.com/question/17146617

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