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Q.
Half-life period of the first order reaction is $100 $ days. After $144.3$ days, concentration of the reactant is reduced to $\ldots \ldots$ of the original value.
Chemical Kinetics
Solution:
$T_{50}=\frac{0.693}{k}$
$\therefore k=\frac{0.693}{t_{50}}=\frac{0.693}{100}$ day $^{-1}$
$\frac{1}{k}=\frac{100}{0.693}=1.44 .3$ days $=$ Average life
Thus, given time $t=\frac{1}{k}$ (Average life)
$C = Coe ^{- kt }= Coe ^{- k / k }=\frac{ Co }{e}$
Thus, concentration is reduced to $\left(\frac{1}{e}\right)$ of the initial value.