A radioactive isotope $X$ with a half-life of $1.37 \times {10^9}$ years decays to $Y$ which is stable. A sample of rock from the moon was found to contain both the elements $X$ and $Y$ which were in the ratio of $1 : 7$. The age of the rock is

Substance $A$ has atomic mass number $16$ and half life of $1$ day. Another substance $B$ has atomic mass number $32$ and half life of $\frac{1}{2}$ day. If both $A$ and $B$ simultaneously start undergo radio activity at the same time with initial mass $320\,g$ each, how many total atoms of $A$ and $B$ combined would be left after $2$ days $.........\times 10^{24}$

If $T$ is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is

The half life of a radioactive substance is $5$ years. After $x$ years a given sample of the radioactive substance gest reduced to $6.25 \%$ of its initial value of $x$ is ...............

A radioactive material of half-life $T$ was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are $A_1$ and $A_2$ respectively then their age difference equals :

Half life of a radioactive substance is $T$. The time taken for all the nuclei to disintegrate will be