At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.

If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

The half-life of a radioactive element is $30$ days. What percentage of the element will have decayed in $90$ days?

Two radioactive substances $X$ and $Y$ initially contain equal number of nuclei. $X$ has a half-life of $1\, hour$ and $Y$ has a half-life of $2\, hours$. After $2\, hours$,the ratio of the activity of $X$ to the activity of $Y$ is

Half-life is measured by

$A$ 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: