After five half-lives, the percentage of original radioactive atoms left is ...... $ \%$

The rate of disintegration of a fixed quantity of a radioactive element can be increased by

$A$ neutron beam has a kinetic energy of $0.0837 \, eV$. Its half-life is $693 \, s$ and its mass is $1.675 \times 10^{-27} \, kg$. What fraction of the neutrons will remain undecayed after traveling a distance of $40 \, m$?

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

The half-life of $Au^{198}$ is $2.7 \, days$. The activity of $1.50 \, mg$ of $Au^{198}$ if its atomic weight is $198 \, g \, mol^{-1}$ is ....... $Ci$ $(N_A = 6 \times 10^{23} \, mol^{-1})$.

In a radioactive decay process,the activity is defined as $A = -\frac{dN}{dt}$,where $N(t)$ is the number of radioactive nuclei at time $t$. Two radioactive sources,$S_1$ and $S_2$,have the same activity at time $t = 0$. At a later time,the activities of $S_1$ and $S_2$ are $A_1$ and $A_2$,respectively. When $S_1$ and $S_2$ have just completed their $3^{\text{rd}}$ and $7^{\text{th}}$ half-lives,respectively,the ratio $A_1/A_2$ is: