$A$ radioactive element has a half-life of $20 \ \text{minutes}$. How much time should elapse before the element is reduced to $\frac{1}{8}$th of the original mass? (Answer in $\text{minutes}$)

$A$ radioactive substance is required to have an activity of $0.01 \mu Ci$ in the human body after $24 \ hours$. The half-life of the radioactive substance is $6 \ hours$. What is the maximum initial activity that can be administered (in $\mu Ci$)?

$A$ sample is obtained from sea water. $11.9$ $C^{14}$ atoms dissociate from $1 \ g$ of carbon. $15.3$ $C^{14}$ atoms dissociate from a live sample. How many years old is the sample? $(t_{1/2} = 5730 \ \text{years})$

What is the order of radioactive decay of a substance?

$A$ first-order nuclear reaction is half-completed in $45 \ minutes$. How long does it take for $99.9\%$ of the reaction to be completed in $hours$?

$2 \text{ g}$ of a radioactive sample having a half-life of $15$ days was synthesized on $1^{st}$ Jan $2009$. The amount of the sample left behind on $1^{st}$ March $2009$ (including both the days) is: (in $\text{ g}$)