The half-life of a radioactive substance is $20 \text{ minutes}$. In $........ \text{ minutes}$ time,the activity of the substance drops to $\left(\frac{1}{16}\right)^{th}$ of its initial value.

$A$ parent nucleus $X$ undergoes $\alpha$-decay with a half-life of $75000 \text{ yrs}$. The daughter nucleus $Y$ undergoes $\beta$-decay with a half-life of $9 \text{ months}$. In a particular sample, it is found that the rate of emission of $\beta$-particles is nearly constant (over several months) at $10^{7} / \text{h}$. What will be the number of $\alpha$-particles emitted in an hour?

The activities of three radioactive substances $A, B$ and $C$ are represented by the curves $A, B$ and $C$ in the figure. Then their half-lives $T_{\frac{1}{2}}(A) : T_{\frac{1}{2}}(B) : T_{\frac{1}{2}}(C)$ are in the ratio:

The half-life period of a radioactive element is $10$ days. How long does it take for $90\%$ of a given mass of this element to disintegrate?

At time $t = 0$,$N_1$ nuclei of decay constant $\lambda_1$ and $N_2$ nuclei of decay constant $\lambda_2$ are mixed. The decay rate of the mixture is:

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is: