The half-life of a radioactive element is $1600$ years. The fraction of the sample that remains undecayed after $6400$ years will be:

The half-life of a radioactive sample,where the initial activity of the material was $8 \text{ counts}$ and after $3 \text{ hours}$ it becomes $1 \text{ count}$,is ............... $hours$.

An element $X$ with a half-life of $1.4 \times 10^9$ years decays to form another stable element $Y$. $A$ sample is taken from a rock that contains both $X$ and $Y$ in the ratio $1:7$. If at the time of formation of the rock,$Y$ was not present in the sample,then the age of the rock in years is

$A$ neutron beam has a kinetic energy of $0.0837 \, eV$. Its half-life is $693 \, s$ and its mass is $1.675 \times 10^{-27} \, kg$. What fraction of the neutrons will remain undecayed after traveling a distance of $40 \, m$?

The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that

The activity of a radioactive sample is measured as $N_0$ counts per minute at $t = 0$ and $N_0/e$ counts per minute at $t = 5 \, minutes$. The time (in $minutes$) at which the activity reduces to half its value is