The half-life of radium is about $1600$ years. Of $100 \, g$ of radium existing now, $25 \, g$ will remain unchanged after .......... $years$.

The half-lives of $X$ and $Y$ are $3 \ min$ and $27 \ min$ respectively. If they have the same activity at a certain instant,find the ratio of the number of excited nuclei of $X$ and $Y$ at that instant.

Half-life of a radioactive substance is $20 \, min$. The time between $20\%$ and $80\%$ decay will be ......... $min$.

The atomic weight of a radioactive element is $M_w$ grams. The radioactivity of $m$ grams of this element is ......... ($N_A$ is Avogadro's number,$\lambda$ is the decay constant).

$90\%$ of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the initial sample will decay in a total time $2t$ : ..............$\%$

$A$ solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda$ is injected into 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 is $300\,decays$ per minute. What is the total volume of blood in the animal's body in litres? (Given: $1\,Ci = 3.7 \times 10^{10}$ decays per second and at $t = 10\,hrs$,$e^{-\lambda t} = 0.84$)