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

$A$ 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 nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text{th}}$ of its initial value in $30\, \text{years}$. The half-life of the radioactive element is $....\, \text{years}$.

Radon $({Rn})$ decays into Polonium $({Po})$ by emitting an $\alpha$-particle with a half-life of $4\, days$. $A$ sample contains $6.4 \times 10^{10}$ atoms of $Rn$. After $12\, days$,the number of atoms of $Rn$ left in the sample will be:

The half-life of a radioactive element is $10 \, days$. The time required for the mass of the sample to reduce to $\frac{1}{10}$ of its initial mass is approximately ........ days.

The half-life of the isotope $_{11}Na^{24}$ is $15 \, hrs$. How much time does it take for $\frac{7}{8}$ of a sample of this isotope to decay?