Half-life period of a sample is $15$ years. How long will it take to decay $96.875\%$ of the sample?

The percentage of ${}^{235}U$ presently on Earth is $0.72\%$ and the rest $(99.28\%)$ may be taken to be ${}^{238}U$. Assume that all uranium on Earth was produced in a supernova explosion long ago with the initial ratio ${}^{235}U / {}^{238}U = 2.0$. How long ago did the supernova event occur? (Take the half-lives of ${}^{235}U$ and ${}^{238}U$ to be $7.1 \times 10^8$ years and $4.5 \times 10^9$ years respectively).

For a certain radioactive process,the graph between $\ln R$ and $t \, (\text{sec})$ is obtained as shown in the figure. Then the value of the half-life for the unknown radioactive material is approximately $.... \, \text{sec}$.

In time $t$,$7/8$ of a radioactive sample disintegrates. How much time will it take for $15/16$ of the sample to disintegrate?

If $10\%$ of a radioactive material decays in $5\, days$,then the amount of the original material left after $20\, days$ is approximately .......... $\%$

The decay constant $\lambda$ of a radioactive sample is the probability of decay of an atom in unit time. Then,