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

The radioactive sources $A$ and $B$ of half lives of $2\, hr$ and $4\, hr$ respectively, initially contain the same number of radioactive atoms. At the end of $2\, hours,$ their rates of disintegration are in the ratio :

The nuclear activity of a radioactive element becomes $\left(\frac{1}{8}\right)^{\text {th }}$ of its initial value in $30\, years.$ The half-life of radioactive element is $....\,years.$

Half lives of two radioactive substances $A$ and $B$ are respectively $20$ minutes and $40$ minutes. Initially the sample of $A$ and $B$ have equal number of nuclei. After $80$ minutes, the ratio of remaining number of $A$ and $B$ nuclei is

The half life of a radioactive isotope $'X'$ is $20$ years, It decays to another element $'Y'$ which is stable. The two elements $'X'$ and $'Y'$ were found to be in  the ratio $1:7$ in a simple of a given rock . The age of the rock is estimated to be............$years$

A small quantity of solution containing $Na^{24}$ radio nuclide of activity $1$ microcurie 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 $296$ disintegration 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 ......... $liter$

(Take $1$ curie $= 3.7 × 10^{10}$ disintegration per second and ${e^{ - \lambda t}} = 0.7927;$ where $\lambda$= disintegration constant)