Identify True $(T)$ and False $(F)$ statements of the following for a first order reaction $R \rightarrow P$.
$(i) \ t_{1/2} \propto [R]_0^0$
$(ii) \ t_{1/2} = \frac{0.693}{k}$

If the half-life $(t_{1/2})$ of a first-order reaction is $20 \ minutes$,what fraction of the reactant remains after $40 \ minutes$?

For a first order reaction $A \to B$,the reaction rate at reactant concentration of $0.01 \ M$ is found to be $2.0 \times 10^{-5} \ mol \ L^{-1} \ s^{-1}$. The half-life period of the reaction is .......... $sec$.

The ratio of the time taken to complete $60\%$ and $20\%$ of a first-order reaction $[A \rightarrow \text{product}]$ is : $(\log 2 = 0.3)$

An organic compound undergoes first-order decomposition. The time taken for its decomposition to $1/8$ and $1/10$ of its initial concentration are $t_{1/8}$ and $t_{1/10}$ respectively. What is the value of $\frac{t_{1/8}}{t_{1/10}} \times 10$? (Given: $\log_{10} 2 = 0.3$)

For a first order reaction $t_{1/2}$ is $1200 \ s$. The specific rate constant in $s^{-1}$ is