The ratio of the number of active nuclei of two different radioactive samples is $2:3$. Their half-lives are $1 \ h$ and $2 \ h$ respectively. The ratio of the number of active nuclei after $6 \ h$ will be:

At a certain time,radioactive elements are taken in the ratio $2:1$. Their half-lives are $12$ hours and $16$ hours respectively. What will be the ratio of the undecayed parts after $2$ days?

$A$ radioactive element has a rate of disintegration of $8000$ disintegrations per minute at a particular instant. After $4$ minutes,it becomes $2000$ disintegrations per minute. The decay constant per minute is: (in $log _e 2$)

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 half-life of a radioactive sample is $T$. The fraction of the initial mass of the sample that decays in an interval $T / 2$ is

The activity of a radioactive sample is $9750$ counts/minute at $t = 0$ and $975$ counts/minute at $t = 5$ minutes. The decay constant is .......... $min^{-1}$.