Half-life is measured by

The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that

$A$ freshly prepared sample of a radioisotope of half-life $1386 \ s$ has activity $10^3$ disintegrations per second. Given that $\ln 2 = 0.693$,the fraction of the initial number of nuclei (expressed in nearest integer percentage) that will decay in the first $80 \ s$ after preparation of the sample is:

Two radioactive materials $A$ and $B$ have decay constants $25 \lambda$ and $16 \lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $B$ to that of $A$ will be $e$ after a time $t = \frac{1}{a \lambda}$. The value of $a$ is $......$

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$, then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

$A$ 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 $\ln 2$)