At any instant,the ratio of the amount of two radioactive substances is $2 : 1$. If their half-lives are $12$ hours and $16$ hours respectively,what will be the ratio of the substances after two days?

For a radioactive material,the half-life is $10$ minutes. If initially there are $600$ nuclei,the time taken (in minutes) for the disintegration of $450$ nuclei is:

If a radioactive material remains $25 \%$ after $16$ days,then its half-life will be ......... days.

Two radioactive nuclei $P$ and $Q$ in a given sample decay into a stable nucleus $R.$ At time $t = 0,$ the number of $P$ species is $4N_0$ and that of $Q$ is $N_0.$ The half-life of $P$ is $1 \text{ minute},$ while that of $Q$ is $2 \text{ minutes}.$ Initially,there are no nuclei of $R$ present in the sample. When the number of nuclei of $P$ and $Q$ are equal,the number of nuclei of $R$ present in the sample would be

$A$ radioactive sample has a half-life of $3$ years. The time required for the activity of the sample to reduce to $\frac{1}{5}$th of its initial value is about (in $years$)

The decay constant of a radioactive sample is $\lambda$. The probability of decay per unit time is: