The half-life period $t_{1/2}$ of a radioactive element is $N$ years. The period of its complete decay is

$A$ 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?

$A$ radioactive isotope has a half-life of $10 \ days$. If today $125 \ mg$ is left over,what was its original weight $40 \ days$ earlier?

$\frac{15}{16}$-th of a radioactive sample decays in $40$ days. The half-life of the sample is ...... days.

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

$^{14}C$ has a half-life of $5760 \ years$. $100 \ mg$ of a sample containing $^{14}C$ is reduced to $25 \ mg$ in ......... $years$.