Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ the number of $P$ species is $4N_0$ and that of $Q$ is $N_0.$ The half-life of $P$ is $1 \text{ minute},$ while that of $Q$ is $2 \text{ minutes}.$ Initially,there are no nuclei of $R$ present in the sample. When the 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 a radioactive sample is $T$. If a fraction $x$ disintegrates in time $t$,what fraction will decay in time $\frac{t}{2}$?

The specific activity of $Ra^{226}$ is $1 \, Ci/g$. The activity of $1 \, \mu g$ of $Ra^{226}$ will be:

The relation between the mean life time $\tau$ and the half-life time $T_{1/2}$ of a radioactive substance is:

Given below are two statements:
Statement $I$: The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is directly proportional to the total number of nuclei in the sample.
Statement $II$: The half-life of a radionuclide is the time required for the number of radioactive nuclei to reduce to half of its initial value at time $t = 0$.
In the light of the above statements, choose the most appropriate answer from the options given below:

$A$ radioactive substance has an average life of $5$ hours. In a time of $5$ hours,