$N$ atoms of a radioactive element emit $n$ number of $\alpha$-particles per second. The mean life of the element in seconds is:

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $(1/e)^2$ after a time interval of:

Plutonium decays with a half-life of $24000 \, \text{years}$. If the plutonium is stored for $72000 \, \text{years}$, then the fraction of plutonium that remains is

After two hours, one-sixteenth of the starting amount of a certain radioactive isotope remained undecayed. The half-life of the isotope is:

Half-lives for $\alpha$ and $\beta$ emission of a radioactive material are $16$ years and $48$ years respectively. When the material decays by giving $\alpha$ and $\beta$ emission simultaneously,the time in which $3/4$th of the material decays is ....... years.

The half-life of a radioactive substance is $3.6$ days. How much of $20\, mg$ of this radioactive substance will remain after $36$ days?