The half-life of radium is $1600$ years. Its mean life will be ....... years.

Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as: (where $\lambda$ is the decay constant)

$A$ radioactive nucleus is being produced at a constant rate $\alpha$ per second. Its decay constant is $\lambda$. If $N_0$ is the number of nuclei at time $t = 0$,then the maximum number of nuclei possible is:

The activity of a sample is $64 \times 10^{-5} \, Ci$. Its half-life is $3 \, days$. The activity will become $5 \times 10^{-6} \, Ci$ after ......... $days$.

The half-life of a radioactive element $A$ is the same as the mean-life of another radioactive element $B.$ Initially, both substances have the same number of atoms, then

$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \ s$ and $10 \ s$ respectively. Initially,the mixture has $40 \ g$ of $A_1$ and $160 \ g$ of $A_2$. The amount of the two in the mixture will become equal after: (in $s$)