The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17} \; s$. If the number of nuclei in the sample is $2.0 \times 10^{21}$,the activity of the sample is nearly:

$A$ 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 isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be

The half-life of $Bi^{210}$ is $5 \ days$. What time is taken by $(7/8)^{th}$ part of the sample to decay?

The sample of a radioactive substance has $10^6$ nuclei. Its half-life is $20 \, s$. The number of nuclei that will be left after $10 \, s$ is nearly ...... $\times 10^5$.

$A$ radioactive sample at any instant has its disintegration rate $5000$ disintegrations per minute. After $5$ minutes,the rate is $1250$ disintegrations per minute. Then,the decay constant (per minute) is (in $, \ln 2$)