The half-life of radioactive $Po$ (Polonium) is $138.6 \, \text{days}$. For $1,000,000$ Polonium atoms, the number of disintegrations in $24 \, \text{hours}$ is:

Two radioactive materials $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t=0$,they have the same number of nuclei. The ratio of the number of nuclei of $A$ to that of $B$ will be $(1/e)^2$ after a time interval of:

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

The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second,whose mean life is $10^9 \ s$. The mass of an atom of this radioisotope is $10^{-25} \ kg$. The mass (in $mg$) of the radioactive sample is

Two radioactive substances $A$ and $B$ have decay constants $5\lambda$ and $\lambda$ respectively. At $t = 0$,a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $(1/e)^2$ will be

The half-life period of a radioactive element $x$ is the same as the mean life time of another radioactive element $y$. Initially,they have the same number of atoms. Then: