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 inversely proportional to the total number of nuclei in the sample. Statement-II: The half life of a radionuclide is the sum of the life time of all nuclei, divided by the initial concentration of the nuclei at time t=0. In the light of the above statements, choose the most appropriate answer from the options given below:

In the nuclear reaction $X(n, \alpha){}_{3}^{7}\mathrm{Li}$, the term $X$ will be:

The half-life of a radioactive sample undergoing $\alpha$-decay is $1.4 \times 10^{17}\text{ s}$. If the number of nuclei in the sample is $2.0 \times 10^{21}$, the activity of the sample is nearly equal to:

If the nuclear radius of $^{27}\text{Al}$ is 3.6 Fermi, the approximate nuclear radius of $^{64}\text{Cu}$ in Fermi is:

The half-life of a radioactive substance is 30 minutes. The time (in minute) taken between 40% decay and 85% decay of the same radioactive substance is:

The fraction of the original number of radioactive atoms that disintegrates (decays) during the average lifetime of a radioactive substance will be:

A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of the radius of two daughter nuclei respectively is:

In the nuclear emission stated above: ${}_{82}^{290}X \xrightarrow{\alpha} Y \xrightarrow{e^+} Z \xrightarrow{\beta^-} P \xrightarrow{e^-} Q$, the mass number and atomic number of the product Q respectively, are:

The energy equivalent of 0.5 g of a substance is: