$x$ fraction of a radioactive sample decays in $t$ time. What fraction will decay in $2t$ time?

The activity of a radioactive substance can be represented by various units. Select the correct option.

The half-life period of a radioactive sample is $3.8 \ days$. After how many days will the sample become $\frac{1}{8}$ of the original substance?

The half-life of the isotope $^{11}Na^{24}$ is $15 \text{ hr}$. How much time does it take for $(7/8)$ of a sample of this isotope to decay (in $\text{ hour}$)?

If the half-life of an element is $69.3 \text{ hours}$,what percentage of it will decay between the $10^{\text{th}}$ and $11^{\text{th}}$ hours? (Initial activity $= 50 \mu Ci$)

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: