$A$ radioactive sample has a half-life of $5$ years. The probability of decay in $10$ years will be ........$\%$

$A$ radioactive source has a half-life of $6 \,h$. $A$ freshly prepared sample of the same exhibits radioactivity $32$ times the permissible safe value. The minimum time after which it would be possible to work safely with the source is (in $\,h$)

At any instant,two elements $X_1$ and $X_2$ have the same number of radioactive atoms. If the decay constants of $X_1$ and $X_2$ are $10\lambda$ and $\lambda$ respectively,then the time when the ratio of their atoms becomes $\frac{1}{e}$ will be:

The decay constant of a radioactive substance is $0.173 \, (years)^{-1}.$ Therefore:

$A$ certain radioactive element disintegrates with a decay constant of $7.9 \times 10^{-10} / s$. At a given instant of time, if the activity of the sample is equal to $55.3 \times 10^{11}$ disintegration/second, then the number of nuclei at that instant of time 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 ...... $\times 10^5$.