The half-life period of a radio-active element $X$ is same as the mean life time of another radio-active element $Y$ Initially they have the same number of atoms. Then

The half life of a radioactive isotope $'X'$ is $20$ years, It decays to another element $'Y'$ which is stable. The two elements $'X'$ and $'Y'$ were found to be in  the ratio $1:7$ in a simple of a given rock . The age of the rock is estimated to be............$years$

There are $10^{10}$ radioactive nuclei in a given radioactive element, Its half-life time is $1\, minute.$ How many nuclei will remain after $30\, seconds?$

$(\sqrt{2}=1.414)$

A solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda $ is injected in an animal's body. If $1 \,cm^3$ of blood is drawn from the animal's body after $10\, hrs$ of injection, the activity found was $300\, decays$ per minute. What is the volume of blood that is flowing in the body?..........$litres$ ( $ICi = 3.7 \times 10^{10}$ decay per second and at $t = 10\, hrs$ ${e^{ - \lambda t}} = 0.84$ )

A sample of radioactive element has a mass of $10\, gm$ at an instant $t = 0$.The approximate mass of this element in the sample after two mean lives is ..........$gm$

If half-life of a radioactive atom is $2.3\, days$, then its decay constant would be