$A$ count rate meter shows a count of $240$ per minute from a given radioactive source. One hour later,the meter shows a count rate of $30$ per minute. The half-life of the source is .......... $min$.

At a given instant,there are $25\%$ undecayed radioactive nuclei in a sample. After $10 \, s$,the number of undecayed nuclei reduces to $6.25\%$. The mean life of the nuclei is...........$ s$.

$A$ small quantity of solution containing $Na^{24}$ radionuclide of activity $1 \, \mu Ci$ is injected into the blood of a person. $A$ sample of the blood of volume $1 \, cm^3$ taken after $5 \, hours$ shows an activity of $296$ disintegrations per minute. What will be the total volume of the blood in the body of the person? Assume that the radioactive solution mixes uniformly in the blood of the person: ............ $L$ (Take $1 \, Ci = 3.7 \times 10^{10}$ disintegrations per second and $e^{-\lambda t} = 0.7927$; where $\lambda$ is the disintegration constant).

$A$ sample of radioactive material $A$,which has an activity of $10\, mCi$ $(1\, Ci = 3.7 \times 10^{10}\, \text{decays/s})$,has twice the number of nuclei as another sample of different radioactive material $B$,which has an activity of $20\, mCi$. The correct choices for half-lives of $A$ and $B$ would then be respectively:

The unit of radioactivity is Rutherford. Its value is:

The radiation emitted by a radioactive substance with a half-life of $30 \ min$ is measured by a Geiger-Muller counter. If the count rate drops to $5 \ \text{disintegrations/sec}$ in $2 \ \text{hours}$, find the initial disintegration rate.