$A$ sample of a radioactive element contains $4 \times 10^{16}$ active nuclei. If the half-life of the element is $10$ days,then the number of decayed nuclei after $30$ days is ........ $\times 10^{16}$.

Ten percent of a radioactive sample has decayed in $1$ day. After $2$ days,the decayed percentage of nuclei will be ...... $\%$

$A$ and $B$ are two radioactive elements. Their half-lives are $1 \, year$ and $2 \, years$ respectively. Initially,$10 \, g$ of $A$ and $1 \, g$ of $B$ are taken. After how many years will their remaining quantities be equal?

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$.

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $(1/e)^2$ after a time interval of:

The radioactivity of a sample is $R_1$ at a time $T_1$ and $R_2$ at a time $T_2$. If the half-life of the specimen is $T$,then the number of atoms that have disintegrated in the time interval $(T_2 - T_1)$ is proportional to