$A$ radioactive element will decay by $99\%$ between which of the following number of half-lives?

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of $C^{14}$ (half-life $= 5700 \, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about .......... $years$.

$A$ radioactive substance is being produced at a constant rate of $10 \text{ nuclei/s}$. The decay constant of the substance is $0.5 \text{ s}^{-1}$. After what time will the number of radioactive nuclei become $10$? Initially,there are no nuclei present. Assume the decay law holds for the sample.

Tritium has a half-life of $12.5\; y$ undergoing beta decay. What fraction of a sample of pure tritium will remain undecayed after $25\; y$?

The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half-life of the specimen is $T,$ the number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to

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: