In a radioactive sample,there are $1.414 \times 10^6$ active nuclei. If they reduce to $10^6$ within $10 \text{ min}$,then the half-life of this sample will be ....... $\text{min}$.

In time $t$,$7/8$ of a radioactive sample disintegrates. How much time will it take for $15/16$ of the sample to disintegrate?

At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$?

The activity of a radioactive substance is $R_1$ at time $t_1$ and $R_2$ at a later time $t_2$. Its decay constant is $\lambda$. Which of the following relations is correct?

For a substance,the average life for $\alpha$-emission is $1620$ years and for $\beta$-emission is $405$ years. After how much time will $1/4$ of the material remain after both $\alpha$ and $\beta$ emissions?

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