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  •  Assuming  of trace radioactive element y with a half life of 45 years is

 Assuming 1 \mathrm{\mu g} of trace radioactive element y with a half life of 45 years is absorbed by growing tree. The amount of 4 remaining in the trees after 1135 years{ Round off to Nearest integers}

Option: 1

10^{-70}


Option: 2

10^{-94}


Option: 3

10^{-8}


Option: 4

10^{-2}


Answers (1)

best_answer

\mathrm{\begin{aligned} \lambda t & =\ln \left(\frac{a}{a-x}\right) \\ t_{1 / 2} & =\frac{\ln 2}{\lambda} \\ \lambda & =\frac{\ln 2}{t_1 / 2} \\ 1135 & =\frac{45}{\ln 2} \ln \left(\frac{1}{\omega}\right) \\ 1135 & =\frac{45}{0.30} \log \left(\frac{1}{\omega}\right) \\ \frac{1135 \times 0.30}{45} & =\log \left(\frac{1}{\omega}\right) \\ 7.5 & =\log \left(\frac{1}{\omega}\right) \end{aligned} }
\mathrm{\begin{aligned} & w=10^{-7.5} \\ & \omega \approx 10^{-8} \end{aligned} }

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