If the half-life of a radioactive element is $3 \ hours$,what fraction of its initial activity remains after $9 \ hours$?

The half-life of a neutron is $693 \ s$. What fraction of neutrons will decay when a beam of neutrons, having kinetic energy of $0.084 \ eV$, travels a distance of $1 \ km$? (mass of neutron $= 1.68 \times 10^{-27} \ kg$, and $\ln 2 = 0.693$)

$A$ radioactive material whose half-life period is $2$ years weighs $1 \,g$ and is stored in the laboratory for $4$ years. Then the amount of remaining radioactive material is (in $\,g$)

If the half-life of a radioactive atom is $2.3 \, days$,then its decay constant would be

$A$ radioactive sample of $U^{238}$ decays to $Pb$ through a process for which the half-life is $4.5 \times 10^9$ years. Find the ratio of the number of nuclei of $Pb$ to $U^{238}$ after a time of $1.5 \times 10^9$ years (given $2^{1/3} = 1.26$).

The number of nuclei of a radioactive substance is $1000$ and $900$ at times $t = 0$ and $t = 2 \ s$,respectively. Then,the number of nuclei at time $t = 4 \ s$ will be: