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?

$A$ certain nuclide has a half-life period of $30 \ minutes$. If a sample containing $600$ atoms is allowed to decay for $90 \ minutes$,how many atoms will remain?

If a substance with a half-life of $3 \ days$ is kept for $12 \ days$,what fraction of the substance remains?

$1.0 \ g$ of radioactive sodium decays to $0.25 \ g$ in $16 \ hours$. Calculate the time required for $48 \ g$ of the same radioactive sodium to decay to $3.0 \ g$. (in $hours$)

To determine the half-life of a radioactive element,a student plots a graph of $\ln|dN(t)/dt|$ versus $t$. Here $dN(t)/dt$ is the rate of radioactive decay at time $t$. If the number of radioactive nuclei of this element decreases by a factor of $p$ after $4.16 \ \text{years}$,the value of $p$ is

The half-life of $_6C^{14}$,if its decay constant is $6.31 \times 10^{-4} \ yr^{-1}$,is ....... $yrs$.