The activity of a radioactive element decreases to one-third of its original activity $R_0$ in $9$ years. After a further $9$ years,its activity will be

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

$A$ parent nucleus $X$ decays into a daughter nucleus $Y$,which in turn decays into $Z$. The half-lives of $X$ and $Y$ are $40000 \, yr$ and $20 \, yr$,respectively. In a certain sample,it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$,the number of $Y$ nuclei present in it is

The half-life of a radioactive sample is $T$. The fraction of the initial mass of the sample that decays in an interval $T / 2$ is

$A$ radioactive sample of half-life $ 10 $ days contains $ 1000x $ nuclei. The number of original nuclei present after $ 5 $ days is: (in $x$)

$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)