The nuclide $^{131}I$ is radioactive,with a half-life of $8.04$ days. At noon on January $1$,the activity of a certain sample is $600 \, Bq$. The activity at noon on January $24$ will be

The radioactive materials $x_1$ and $x_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $x_1$ to that of $x_2$ will be $1/e$ after a time $t$ equal to:

For a radioactive element,the mean life is $\tau$. At time $t = 0$,the number of nuclei decaying per unit time is $n$. The number of nuclei that have decayed between time $0$ and $t$ is:

If $87.5 \%$ of atoms of a radioactive element decay in $6 \ days$, then the fraction of atoms of the element that decay in $8 \ days$ is

The initial activity of a certain radioactive isotope was measured as $16000 \ counts \ min^{-1}$. Given that the only activity measured was due to this isotope and that its activity after $12 \ h$ was $2000 \ counts \ min^{-1}$,its half-life,in hours,is nearest to

Draw a graph showing the variation of decay rate with the number of active nuclei.