Two radioactive nuclei $P$ and $Q,$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ number of $P$ species are $4\,\, N_0$ and that of $Q$ are $N_0$. Half-life of $P$ (for conversion to $R$) is $1$ minute where as that of $Q$ is $2$ minutes. Initially there are no nuclei of $R$ present in the sample. When number of nuclei of $P$ and $Q$ are equal, the number of nuclei of $R$ present in the sample would be

The half life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

A radioactive nucleus can decay by two different processes. Half-life for the first process is $3.0\, hours$ while it is $4.5\, hours$ for the second process. The effective half- life of the nucleus will be $………\,hours.$

In a radioactive material, fraction of active material remaining after time $t$ is $\frac{9}{16}$ The fraction that was remaining after $\frac{t}{2}$ is 

Radioactivity was discovered by