$A$ radioactive substance emits $100$ beta particles in the first $2 \,s$ and $50$ beta particles in the next $2 \,s$. The mean life of the sample is

$A$ certain radioactive substance has a half-life of $5\, years$. Thus, for a nucleus in a sample of the element, the probability of decay in $10\, years$ is ......... $\%$

The half-life period of element $X$ is same as the mean life time of element $Y$. Assume initially $X$ and $Y$ have same number of atoms. Then

The half-life of $^{238}_{92}U$ undergoing $\alpha$-decay is $4.5 \times 10^{9} \text{ years}$. What is the activity of a $1 \text{ g}$ sample of $^{238}_{92}U$?

In a radioactive element,the fraction of the initial amount remaining after its mean lifetime is:

$A$ radioactive material decays by simultaneous emissions of two particles with half-lives of $1400 \, years$ and $700 \, years$ respectively. What will be the time after which one-third of the material remains? (Take $\ln 3 = 1.1$) (In $years$)