The half-life of a radioactive nuclide is $100 \, hours$. The fraction of original activity that will remain after $150 \, hours$ would be:

$A$ radioactive sample decays by two modes: $\alpha$-decay and $\beta$-decay. $66.6\%$ of the time it decays by $\alpha$-decay and $33.3\%$ of the time it decays by $\beta$-decay. If the effective half-life of the sample is $60 \text{ years}$,what will be the half-life of the sample if it decays only by $\alpha$-decay? (in years)

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

Half-life period of a sample is $15$ years. How long will it take to decay $96.875\%$ of the sample?

Draw a graph showing the variation of decay rate with the number of active nuclei.

$A$ radioactive element decays to form a stable nuclide. The rate of decay of the reactant $\left( \frac{dN}{dt} \right)$ will vary with time $(t)$ as shown in which figure?