$A$ sample of a radioactive element has a mass of $10 \, g$ at an instant $t = 0$. The approximate mass of this element in the sample after two mean lives is .......... $g$.

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 $1 \; g$?

The half-life period of a radioactive sample is $T$. If a fraction $x$ disintegrates in time $t$,what fraction will decay in time $\frac{t}{2}$?

The graph shows the $\log$ of activity $\log R$ of a radioactive material as a function of time $t$ in minutes. The half-life (in minutes) for the decay is closest to

Radioactive nuclei $A$ and $B$ disintegrate into $C$ with half-lives $T$ and $2T$. At $t = 0$,the number of nuclei of each $A$ and $B$ is $x$. The number of nuclei of $C$ when the rate of disintegration of $A$ and $B$ are equal is:

Find the time in years required for $10\%$ of a radioactive sample to decay,given that its half-life is $22 \text{ years}$.