There are two radionuclei $A$ and $B.$ $A$ is an alpha emitter and $B$ is a beta emitter. Their distintegration constants are in the ratio of $1 : 2.$ What should be the ratio of number of atoms of two at time $t = 0$ so that probabilities of getting $\alpha$ and $\beta$ particles are same at time $t = 0.$

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 $t = 10\, hrs$ ${e^{ – \lambda t}} = 0.84$ )

The half-life of a radioactive substance is $48$ hours. How much time will it take to disintegrate to its $\frac{1}{{16}} \,th$ part …………$hour$

At $t = 0$, number of active nuclei in a sample is $N_0$. How much no. of nuclei will decay in time between its first mean life and second half life?

For a substance the average life for $\alpha $ -emission is $1620\ years$ and for $\beta $ emission is $405\ years$ . After how much time the $\frac {1}{4}$ of the material remains by simultaneous emission ………… $years$