The radioactivity due to the $^{14}C$ isotope (half-life $6000 \ years$) of a sample of wood from an ancient tomb was found to be nearly half that of fresh wood. The tomb is therefore about ........... years old.

The amount of $_{53}I^{128}$ $(t_{1/2} = 25 \ min)$ remaining after $75 \ min$ is:

The half-life period of a radioactive substance is $8 \ years$. After $16 \ years$,the mass of the substance will reduce from starting $16.0 \ g$ to ....... $g$.

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

$A$ radioactive element decays at such a rate that after $15 \ min$ only $1/10$ of the original amount is left. How many more minutes will be needed when only $1/100$ of the original amount will be left? .......... $\min$

$A$ piece of wood from an archaeological sample has $5.0 \text{ counts min}^{-1} \text{ g}^{-1}$ of $^{14}C$,while a fresh sample of wood has a count of $15.0 \text{ counts min}^{-1} \text{ g}^{-1}$. If the half-life of $^{14}C$ is $5770 \text{ yr}$,the age of the archaeological sample is: