A radioactive substance decays for a period equal to its average life. The remaining fraction is:

The mass of one curie of ${\mathrm{U}}^{234}$ is:

($1$ curie$=3.7\times {10}^{10}$ disintegration/second)

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life $18$ days inside the laboratory Tests revealed that the radiation was $64$ times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

Two radioactive materials $A$ and $B$ 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 $A$ to that of $B$ will be $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$e$}\right.$ after a time:

Half-lives of two radioactive nuclei $A$ and $B$ are $10$ minutes and $20$ minutes, respectively. If initially a sample has equal number of nuclei, then after $60$ minutes, the ratio of decayed numbers of nuclei $A$ and $B$ will be:

At a given instant, say $t=0$, two radioactive substances $A$ and $B$ have equal activities. The ratio $\frac{R_B}{R_A}$ of their activities after time $t$ itself decays with time $t$ as $e^{-3t}$. If decay constant of $A$ is $1$, the half-life of $B$ is:

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At $t=0$ it was $1600$ counts per second and $t =8$ seconds it was $100$ counts per second. The count rate observed, as counts per second, at $t=6$ seconds is close to: