A sample of radioactive material $A$, that has an activity of $10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)$, has twice the number of nuclei as another sample of different radioactive material $B$ which has an activity of $20\, mCi$. The correct choices for half-lives of $A$ and $B$ would then be respectively

The radioactivity of a sample is $R_1$ at time $T_1$ and $R_2$ at time $T_2.$ If the half life of the specimen is $T.$ Number of atoms that have disintegrated in time $(T_2 - T_1)$ is proportional to

The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is $5\; days$. The activity will become $5 \times 10^{-6}$ curie after $.......day$

Two radioactive isotopes $P$ and $Q$ have half Jives $10$ minutes and $15$ minutes respectively. Freshly prepared samples of each isotope initially gontain the same number of atoms. After $30$ minutes, the ratio $\frac{\text { number of atoms of } P}{\text { number of atoms of } Q}$ will be

Consider an initially pure $M$ gm sample of$_ A{X}$, an isotope that has a half life of $T$ hour, what is it’s initial decay rate ($N_A$ = Avogrado No.)

A radio-isotope has a half- life of $5$ years. The fraction of the atoms of this material that would decay in $15$ years will be