During the mean life of a radioactive element,the fraction that disintegrates is

Consider an initially pure $M \text{ g}$ sample of an isotope $X$ with mass number $A$,which has a half-life of $T \text{ hours}$. What is its initial decay rate? ($N_A$ = Avogadro number)

The half-life of a radioactive substance is $12 \text{ minutes}$. The time gap between $28 \%$ decay and $82 \%$ decay of the radioactive substance is

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

$A$ radioactive sample decays at a rate of $5000$ disintegrations/minute at a certain instant. After $5$ minutes, the rate becomes $1250$ disintegrations/minute. The decay constant is ....... (in $\ln 2$)

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta$-emission respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,the time after which only one-fourth of the sample remains is: