$A$ 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:

What fraction of a radioactive material will get disintegrated in a period of two half-lives?

Two radioactive elements $R$ and $S$ disintegrate as:
$R \rightarrow P + \alpha; \lambda_R = 4.5 \times 10^{-3} \, \text{years}^{-1}$
$S \rightarrow P + \beta; \lambda_S = 3 \times 10^{-3} \, \text{years}^{-1}$
Starting with the number of atoms of $R$ and $S$ in the ratio of $2:1$,what will be this ratio after the lapse of three half-lives of $R$?

The ratio of the number of active nuclei of two different radioactive samples is $2:3$. Their half-lives are $1 \ h$ and $2 \ h$ respectively. The ratio of the number of active nuclei after $6 \ h$ will be:

The half-life period of a radioactive substance is $60 \ days$. The time taken for $\frac{7}{8}$ of its original mass to disintegrate will be $...... \ days$.

After $280$ days,the activity of a radioactive sample is $6000 \, dps$. The activity reduces to $3000 \, dps$ after another $140$ days. The initial activity of the sample in $dps$ is