The count rate of $10\,g$ of radioactive material was measured at different times and this has been shown in the figure. The half life of material and the total counts (approximately) in the first half life period, respectively are

The half life period of radium is $1600$ years. The fraction of a sample of radium that would remain after $6400$ years is

The sample of a radioactive substance has $10^6$ nuclei. Its half life is $20 \,s$. The number of nuclei that will be left after $10 \,s$ is nearly ...... $\times 10^5$

At any instant, two elements $X _1$ and $X _2$ have same number of radioactive atoms. If the decay constant of $X _1$ and $X _2$ are $10 \lambda$ and $\lambda$ respectively. then the time when the ratio of their atoms becomes $\frac{1}{e}$ respectively will be

The decay constants of a radioactive substance for $\alpha $ and $\beta $ emission are ${\lambda _\alpha }$ and ${\lambda _\beta }$ respectively. If the substance emits $\alpha $ and $\beta $ simultaneously, then the average half life of the material will be

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