Assuming $1 \,\mu \mathrm{g}$ 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 ______ $\times\, 10^{-1} \mu \mathrm{g}$.
[Given : ln 10 = 2.303; log 2 = 0.30]
Answer (integer)
1
Solution
$t=\frac{1}{\lambda} \ln \left(\frac{a}{a-x}\right)$
<br/><br/>
$$
\begin{aligned}
&\Rightarrow100=\left(\frac{30}{\ln 2}\right)\left[\ln \left(\frac{1}{w}\right)\right] \\
&\Rightarrow{\left[\frac{100 \times \log 2}{30}\right]=\log \left(\frac{1}{w}\right)} \\
&\Rightarrow1=\log \left(\frac{1}{w}\right) \\
&\Rightarrow\frac{1}{w}=10 \\
&\text { So } w=0.1 \mu g
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: Chemical Kinetics · Topic: Rate of Reaction
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