The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is

The relation between half-life $(T)$ and decay constant $(\lambda)$ is

The mean lives of a radioactive sample are $30$ years and $60$ years for $\alpha$-emission and $\beta$-emission respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,the time after which only one-fourth of the sample remains is:

The mean lives of a radioactive sample are $30 \, years$ and $60 \, years$ for $\alpha$-emission and $\beta$-emission,respectively. If the sample decays by both $\alpha$-emission and $\beta$-emission simultaneously,then the time after which only one-fourth of the sample remains is approximately ............ $years$.

The half-life of a stream of radioactive particles moving along a straight path with a constant kinetic energy of $4 \text{ eV}$ is $1 \text{ minute}$. The percentage of particles which decay before travelling a distance of $3.6 \text{ km}$ is (Mass of the radioactive particles $= 3.2 \times 10^{-21} \text{ kg}$ and charge of the electron $= 1.6 \times 10^{-19} \text{ C}$).

$A$ radioactive material has a half-life of $10$ days. What fraction of the material would remain after $30$ days?