The Carbon-$14$ dating method is based on the fact that:

During a nuclear explosion,one of the products is $^{90}Sr$ with a half-life of $6.93 \; \text{years}$. If $1 \; \mu g$ of $^{90}Sr$ was absorbed in the bones of a newly born baby in place of $Ca$,how much time,in years,is required to reduce it by $90 \%$ if it is not lost metabolically?

The ratio of $\frac{{}^{14}C}{{}^{12}C}$ in a piece of wood is $\frac{1}{8}$ part that of the atmosphere. If the half-life of ${}^{14}C$ is $5730 \text{ years}$,the age of the wood sample is $.....$ years.

An element has a half-life of $1600 \ years$. The fraction of the mass left after $6400 \ years$ will be:

$A$ piece of wood was found to have the $C^{14}/C^{12}$ ratio $0.7$ times that in a living plant. The time period when the plant died is ....... $years$ (Half-life of $C^{14} = 5760 \, yrs$).

Radioactivity of a sample $(Z=22)$ decreases by $90 \%$ after $10 \ years$. What will be the half-life of the sample (in $years$)?