$A$ radioactive material of half-life $2.5$ hours emits radiation that is $32$ times the safe maximum level. The time (in hours) after which the material can be handled safely is

Two radioactive materials $X_1$ and $X_2$ have decay constants $10 \lambda$ and $\lambda$ respectively. If initially they have the same number of nuclei,then the ratio of the number of nuclei of $X_1$ to that of $X_2$ will be $1 / e$ after a time:

Two radioactive nuclei $A$ and $B$ both convert into a stable nucleus $C$. At time $t = 0$,the number of nuclei of $A$ is $4N_0$ and that of $B$ is $N_0$. The half-life of $A$ is $1 \, min$ and that of $B$ is $2 \, min$. Initially,the number of nuclei of $C$ is zero. At what time are the rates of disintegration of $A$ and $B$ equal?

If the radioactive decay constant of radium is $1.07 \times 10^{-4}$ per year,then its half-life period is approximately equal to ......... $years$.

In one average lifetime of a radioactive nucleus,

In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at an instant of time equal to its mean life is: