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  4. Assuming 1 μ g of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is × 10-1 μ g. [Given: ln 10=2.303 ; log 2=0.30]

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Q. Assuming $1 \mu g$ of trace radioactive element $X$ with a half life of 30 years is absorbed by a growing tree. The amount of $X$ remaining in the tree after 100 years is ___$\times 10^{-1} \mu g$.
[Given : $\ln 10=2.303 ; \log 2=0.30]$

JEE MainJEE Main 2022Chemical Kinetics

Solution:

$t =\frac{1}{\lambda} \ln \left(\frac{ a }{ a - x }\right)$
$ 100=\frac{30}{\ell n 2} \ln \left(\frac{1}{ w }\right)$
$ \frac{1}{ w }=10$
$ W =0.1 \times \mu g$
Ans. $1 \times 10^{-1} \mu g$