The half-life period for a radioactive substance is $15$ minutes. How many grams of this radioactive substance is decayed from $50$ g of substance after $1$ hour?

$A$ piece of wood from an archaeological sample has $5.0 \text{ counts min}^{-1} \text{ g}^{-1}$ of $^{14}C$, while a fresh sample of wood has a count of $15.0 \text{ counts min}^{-1} \text{ g}^{-1}$. If the half-life of $^{14}C$ is $5770 \text{ yr}$, the age of the archaeological sample is:

The half-life of $10 \ g$ of a radioactive substance is $10 \ days$. The half-life of $20 \ g$ of the same substance is .......... $days$.

Initial mass of a radioactive element is $40 \ g$. How many grams of it would be left after $24 \ years$,if its half-life period is $8 \ years$?

If $2.0 \ g$ of a radioactive substance has a half-life of $7 \ days$,what is the half-life of a $1 \ g$ sample?

If the half-life of an isotope $X$ is $10 \ yr$,its decay constant is (in $yr^{-1}$)