Half-life of a radioactive element is $10 \, days$. The time during which the quantity remains $1/10$ of the initial mass will be ......... $days$.

If $T$ is the half-life of a radioactive material,then the fraction that would remain after a time $\frac{T}{2}$ is

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

$A$ sample initially contains $10^{20}$ radioactive atoms. The number of $\alpha$-particles emitted in the third year is $0.3$ times the number of $\alpha$-particles emitted in the second year. How many $\alpha$-particles are emitted in the first year?

An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of $18$ days inside the laboratory. Tests revealed that the radiation level was $64$ times higher than the permissible level required for safe operation. What is the minimum number of days after which the laboratory can be considered safe for use?

$A$ 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 $40 \, m$?