If $n_t$ number of radioatoms are present at time $t$, the following expression will be a constant:

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

$1.0 \ g$ 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 $hours$)

The half-life of a radionuclide is $69.3 \text{ minutes}$. What is its average life (in minutes)?

$87.5\%$ decomposition of a radioactive substance completes in $3$ hours. What is the half-life of that substance?

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