$A$ fresh radioactive sample is given at $t = 0$. Its decay fraction is $\frac{1}{5}$ at $t_1$ instant and $\frac{4}{5}$ at $t_2$ instant. Its mean life is

From $N$ atoms of a radioactive element,$n$ alpha particles are emitted per second. The half-life of the element is ......

The half-life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

The half-life of a radioactive element $X$ is equal to the mean life of another radioactive element $Y$. Initially, the number of atoms for both is the same. Then:

Two radioactive materials $R_1$ and $R_2$ have decay constants $6 \lambda$ and $\lambda$, respectively. The half-life of $R_2$ is $1.4 \times 10^{17} \,s$. Initially, they contain the same number of nuclei. The time at which the ratio of the remaining nuclei of $R_2$ to that of $R_1$ will be $e$ is (Let $\ln 2 = 0.7$):

If the half-life of a radioactive nucleus is $3$ days, nearly what fraction of the initial number of nuclei will decay on the third day? (Given, $\sqrt[3]{0.25} \approx 0.63$)