The half-life of a first-order reaction is $69.35 \, \text{sec}$. The value of the rate constant of the reaction is .......... $\sec^{-1}$.

For the first order reaction $A \rightarrow 2B$,$1 \ mole$ of reactant $A$ gives $0.2 \ moles$ of $B$ after $100 \ minutes$. The half-life of the reaction is $..... \ min$. [Use: $\ln 2 = 0.69, \ln 10 = 2.3$]

$A$ first order reaction has a rate constant of $1 \times 10^{-2} \ s^{-1}$. How much time will it take for $20 \ g$ of reactant to reduce to $5 \ g$ (in $s$)?

For a first order reaction,the time required for completion of $90 \%$ reaction is '$x$' times the half life of the reaction. The value of '$x$' is $........$. (Given: $\ln 10 = 2.303$ and $\log 2 = 0.3010$)

If the half-life period of a first order reaction is $138.6 \ minutes$,then the value of the decay constant for the reaction will be:

$A$ radioactive substance decomposes such that after $100 \ min$,its concentration becomes $1/8$ of the original concentration. Calculate the rate constant $(k)$ and half-life time $(t_{1/2})$.