In a sample of radioactive material,what percentage of the initial number of active nuclei will decay during one mean life?

One mole of radium has an activity of $\frac{1}{3.7} \text{ kilo curie}$. Its decay constant is (Avogadro number $= 6 \times 10^{23} \text{ mol}^{-1}$)

The half-life of a radioactive substance is $5$ years. What is the probability of decay of this element in $10$ years?

The half-life of a radioactive substance is $20 \, \text{minutes}$. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{3}{4}$ of it has decayed and time $t_1$ when $\frac{1}{4}$ of it has decayed is:

$A$ and $B$ are two radioactive elements. The mixture of these elements shows a total activity of $1200 \text{ disintegrations/minute}$. The half-life of $A$ is $1 \text{ day}$ and that of $B$ is $2 \text{ days}$. What will be the total activity after $4 \text{ days}$? Given,the initial number of atoms in $A$ and $B$ are equal.

The half-life of ${}^{198} {Au}$ is $3 \, \text{days}$. If the atomic weight of ${}^{198} {Au}$ is $198 \, \text{g/mol}$, then the activity of $2 \, \text{mg}$ of ${}^{198} {Au}$ is ..... $\times 10^{12} \, \text{disintegration/second}$.