The half-life of a substance is $20 \ min$. The time taken between $33\%$ decay and $67\%$ decay will be ....... $min$.

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.

$A$ 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:

The decay of a radioactive material is shown in the graph. From the graph,the decay constant of the material is nearly (in $h^{-1}$)

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half-lives $1$ month and $2$ months respectively. At time $t=0$,the number of nuclei of each $P$ and $Q$ is $x$. At the time when the rates of disintegration of $P$ and $Q$ are equal,the number of nuclei of $R$ is ........ $x$.

$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \, s$ and $10 \, s$ respectively. Initially,the mixture has $40 \, g$ of $A_1$ and $160 \, g$ of $A_2$. The amount of the two in the mixture will become equal after ......... $s$.