The half-life of a radioactive sample is $20 \ days$. This means that:

At time $t=0$ some radioactive gas is injected into a sealed vessel. At time $T$ some more of the gas is injected into the vessel. Which one of the following graphs best represents the logarithm of the activity $A$ of the gas with time $t$?

The decay constant of a radioactive sample is $\lambda$. The probability of decay per unit time is:

$C^{14}$ has a half-life of $5700$ years. At the end of $11400$ years,the actual amount left is:

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

In a radioactive substance at $t = 0$,the number of atoms is $8 \times 10^4$. Its half-life period is $3 \ years$. The number of atoms $1 \times 10^4$ will remain after an interval of ........... $years$.