$A$ radioactive material has a half-life of $8$ years. The activity of the material will decrease to about $1/8$ of its original value in .......... $years$.

The count rate of $10\,g$ of radioactive material was measured at different times and this has been shown in the figure. The half-life of the material and the total counts (approximately) in the first half-life period,respectively,are:

$A$ radioactive substance of half-life $138.6 \text{ days}$ is placed in a box. After $n$ days, only $20\%$ of the substance is present. Then the value of $n$ is $[\ln(5) = 1.61]$.

$A$ radioactive sample has a half-life of $5 \text{ years}$. The percentage of the fraction decayed in $10 \text{ years}$ will be: (in $\%$)

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

The half-lives of $X$ and $Y$ are $3 \ min$ and $27 \ min$ respectively. If they have the same activity at a certain instant,find the ratio of the number of excited nuclei of $X$ and $Y$ at that instant.