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 $………\times 10^{24}$

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$

The ratio activity of an element becomes $\frac{{1}}{{64}} th$ of its original value in $60\, sec$. Then the half life period is …………$sec$

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

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