$A$ 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.

The half-lives of two radioactive materials $A$ and $B$ are $T$ and $2T$ respectively. If the ratio of the initial masses of the materials $A$ and $B$ is $8:1$, then the time after which the ratio of the masses of the materials $A$ and $B$ becomes $4:1$ is

The decay constant of a radioactive element is $0.01 \ s^{-1}$. Its half-life period is ....... $s$.

In the figure,$X$ represents time and $Y$ represents the activity of a radioactive sample. Then the activity of the sample varies with time according to the curve:

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:

$A$ mixture consists of two radioactive materials $A_1$ and $A_2$ with half-lives of $20 \ s$ and $10 \ s$ respectively. Initially,the mixture has $40 \ g$ of $A_1$ and $160 \ g$ of $A_2$. The amount of the two in the mixture will become equal after: (in $s$)