The activity of a radioactive sample reduces from $A_0$ to $\frac{A_0}{\sqrt{3}}$ in $1$ hour. What will be the activity after $3$ hours more?

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^9 \; s$ is $10^{10} \; s^{-1}$. The number of radioactive atoms in that sample at that instant is,

The half-life of radium is $1600 \, \text{years}$. The fraction of the radium sample that will remain after $6400 \, \text{years}$ is:

Two radioactive materials $X_1$ and $X_2$ have decay constants $5 \lambda$ and $\lambda$ respectively. Initially,they have the same number of nuclei. After time $t$,the ratio of the number of nuclei of $X_1$ to that of $X_2$ is $\frac{1}{e}$. Then $t$ is equal to:

At some instant,a radioactive sample $S_1$ having an activity $5\,\mu Ci$ has twice the number of nuclei as another sample $S_2$ which has an activity of $10\,\mu Ci$. The half-lives of $S_1$ and $S_2$ are:

Two radioactive isotopes $P$ and $Q$ have half-lives $10 \text{ minutes}$ and $15 \text{ minutes}$ respectively. Freshly prepared samples of each isotope initially contain the same number of atoms. After $30 \text{ minutes}$,the ratio $\frac{\text{number of atoms of } P}{\text{number of atoms of } Q}$ will be