The half-life of a radioactive sample,where the initial activity of the material was $8 \text{ counts}$ and after $3 \text{ hours}$ it becomes $1 \text{ count}$,is ............... $hours$.

Two radioactive substances $A$ and $B$ have the same number of initial nuclei. If the half-lives of $A$ and $B$ are $1.5 \ days$ and $4.5 \ days$ respectively,then the ratio of the number of nuclei remaining in $A$ and $B$ after $9 \ days$ is

$A$ radioactive isotope $X$ has a half-life of $20$ years and decays into a stable element $Y$. In a given rock sample, the ratio of the amounts of $X$ and $Y$ is found to be $1:7$. The estimated age of the rock is ......... years.

In a radioactive disintegration,the ratio of the initial number of atoms to the number of atoms present at time $t = \frac{1}{2 \lambda}$ is $[\lambda = \text{decay constant}]$

The half-life of a radioactive element is $12.5 \; h$ and its initial quantity is $256 \; g$. After how much time (in $h$) will its quantity remain $1 \; g$?

The half-life of $^{131}I$ is $8 \, days$. Given a sample of $^{131}I$ at time $t = 0$,we can assert that