The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

If there is $0.1 \ mg$ of radioactive $Th^{234}$, how much of it will remain undecayed after $120 \ \text{days}$, given its half-life is $24 \ \text{days}$? (Answer in $\mu g$)

If $f$ denotes the ratio of the number of nuclei decayed $(N_{d})$ to the number of nuclei at $t=0$ $(N_{0})$,then for a collection of radioactive nuclei,the rate of change of $f$ with respect to time is given as: [$\lambda$ is the radioactive decay constant]

The half-life of a radioactive element is $10 \ h$. The fraction of initial radioactivity of the element that will remain after $40 \ h$ is

$A$ radioactive element having a half-life of $30 \ min$ is undergoing beta decay. The fraction of the radioactive element that remains undecayed after $90 \ min$ will be:

$A$ radioactive substance of mass $10 \, g$ is kept in an open container. What is the approximate mass of the substance remaining in the container after two mean lives (in $, g$)?