$A$ 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 decay constant of radium is $\lambda$. By a suitable process,its compound radium bromide is obtained. The decay constant of radium bromide will be:

In a radioactive material,the fraction of active material remaining after time $t$ is $\frac{9}{16}$. The fraction that was remaining after $\frac{t}{2}$ is:

The half-life of a radioactive substance is $30 \text{ minutes}$. The time taken between $40 \%$ decay and $85 \%$ decay of the same radioactive substance is

Two radioactive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to those of $B$ will be $(1/e)^2$ after a time interval of:

$A$ radioactive sample decays at a rate of $5000$ disintegrations/minute at a certain instant. After $5$ minutes, the rate becomes $1250$ disintegrations/minute. The decay constant is ....... (in $\ln 2$)