The half-life of ${ }_{84}^{209} Po$ is $103 \text{ years}$. The time it takes for a $100 \text{ g}$ sample of ${ }_{84}^{209} Po$ to decay to $3.125 \text{ g}$ is

The masses of two radioactive substances are same and their half-lives are $1 \ yr$ and $2 \ yr$ respectively. The ratio of their activities after $4 \ yr$ will be

Write down the definition and formula of half-life of a radioactive substance.

$A$ piece of wood from a recently cut tree shows $20$ decays per minute. $A$ wooden piece of the same size placed in a museum (obtained from a tree cut many years back) shows $2$ decays per minute. If the half-life of $C^{14}$ is $5730$ years,then the age of the wooden piece placed in the museum is approximately ........... years.

$A$ parent nucleus $X$ decays into a daughter nucleus $Y$,which in turn decays into $Z$. The half-lives of $X$ and $Y$ are $40000 \, yr$ and $20 \, yr$,respectively. In a certain sample,it is found that the number of $Y$ nuclei hardly changes with time. If the number of $X$ nuclei in the sample is $4 \times 10^{20}$,the number of $Y$ nuclei present in it is

$A$ 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 ......... $\%$