"81 years" would be the time must elapse before the safe level is reached.
According to the question,
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.
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