$A$ radioactive element has a half-life period of $800$ years. After $6400$ years,what fraction of the initial amount will remain?

If $t_{1/2}$ is the half-life of a substance,then $t_{3/4}$ is the time in which the substance:

An archaeologist analyses the wood in a prehistoric structure and finds that the ratio of $C^{14}$ (half-life $= 5700 \, years$) to $C^{12}$ is only one-fourth of that found in the cells of buried plants. The age of the wood is about .......... $years$.

$A$ radioactive sample is undergoing $\alpha$ decay. At any time $t_{1}$,its activity is $A$ and at another time $t_{2}$,the activity is $\frac{A}{5}$. What is the average life time for the sample?

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.

Two samples $A$ and $B$ contain equal amount of radioactive substances. If $(1/8)^{th}$ of sample $A$ and $(1/128)^{th}$ of sample $B$ remain after $9 \text{ hours}$, then the ratio of half-life period of $B$ to that of $A$ is