The count rate of a Geiger-Muller counter for the radiation of a radioactive material with a half-life of $30\, minutes$ decreases to $5\, s^{-1}$ after $2\, hours$. The initial count rate was..........$s^{-1}$.

The rate of disintegration of a radioactive sample is $R$ and the number of atoms present at any time $t$ is $N$. When $\frac{R}{N}$ is taken along the $Y$-axis and $t$ is taken along the $X$-axis,the correct graph is:

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 $t$?

If $T$ is the half-life of a radioactive substance,then its instantaneous rate of change of activity is proportional to

The activity of a radioactive sample is measured as $N_0$ counts per minute at time $t = 0$ and $N_0/e$ counts per minute at time $t = 3 \text{ minute}$. The time (in minute) in which the activity reduces to half the value, is

The age of a tree is determined using the radio-isotope of: