Starting with a sample of pure ${}^{66}Cu$, $7/8$ of it decays into $Zn$ in $15 \ minutes$. The corresponding half-life is ................ $minutes$.

$A$ radioactive element decays to form a stable nuclide. The graph representing the number of radioactive nuclei $(N)$ versus time $(t)$ is:

$A$ radioactive material decays by simultaneous emissions of two particles with half-lives of $1400 \, years$ and $700 \, years$ respectively. What will be the time after which one-third of the material remains? (Take $\ln 3 = 1.1$) (In $years$)

$A$ 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 $, g$)?

Radioactive nuclei $P$ and $Q$ disintegrate into $R$ with half-lives $1$ month and $2$ months respectively. At time $t=0$,the number of nuclei of each $P$ and $Q$ is $x$. At the time when the rates of disintegration of $P$ and $Q$ are equal,the number of nuclei of $R$ is ........ $x$.

The half-life of polonium is $140 \, days$. After how many days will $16 \, g$ of polonium be reduced to $1 \, g$ (or $15 \, g$ will decay)?