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

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

What is the relationship between the decay constant $\lambda$ and the half-life $\tau_{1/2}$?

The graph represents the decay of a newly prepared sample of radioactive nuclide $X$ to a stable nuclide $Y$. The half-life of $X$ is $t$. The growth curve for $Y$ intersects the decay curve for $X$ after time $T$. What is the time $T$?

Two radioactive materials $A$ and $B$ having decay constants $7 \lambda$ and $\lambda$ respectively,initially have the same number of nuclei. The time taken for the ratio of the number of nuclei of material $B$ to that of $A$ to be $e$ is:

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)