A radio isotope $X$ with a half-life $1.4 \times 10^{9}\; years$ decays of $Y$ which is stable. A sample of the rock from a cave was found to contain $X$ and $Y$ in the ratio $1: 7$. The age of the rock is …….. $ \times 10^9\; years$

$N$ atoms of a radioactive element emit $n$ alpha particles per second. The half life of the element is

The graph in figure shows how the count-rate $A$ of a radioactive source as measured by a Geiger counter varies with time $t.$ The relationship between $A$ and $t$ is : $($ Assume $ln\,\, 12 = 2.6)$

In a radioactive substance at $t = 0$, the number of atoms is $8 \times {10^4}$. Its half life period is $3$ years. The number of atoms $1 \times {10^4}$ will remain after interval ………..$years$

A radio-active material is reduced to $1 / 8$ of its original amount in $3$ days. If $8 \times 10^{-3}\,kg$ of the material is left after $5$ days. The initial amount of the material is $…….\,g$