Consider a radioactive material of half-life $1.0 \, \text{minute}$. If one of the nuclei decays now,the next one will decay

The half-life of a radioactive element is $1600$ years. The fraction of the sample that remains undecayed after $6400$ years will be:

The half-life of polonium is $140 \, days$. After how many days will $16 \, g$ of polonium be reduced to $1 \, g$ (or $15 \, g$ will decay)?

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$, they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

The half-life of radioactive Polonium $(Po)$ is $138.6$ days. For $10^6$ Polonium atoms,the number of disintegrations in $24$ hours is:

$A$ 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?