For a radioactive material, half-life is $10$ minutes. If initially there are $600$ number of nuclei, the time taken (in minutes) for the disintegration of $450$ nuclei is

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)

A freshly prepared radioactive source of half life $2$ hours $30$ minutes emits radiation which is $64$ times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

In saloons, there is always a characteristics smell due to the ammonia-based chemicals used in hair dyes and other products. Assume the initial concentration of ammonia molecules to be $1000 \,molecules/ m ^3$. Due to air ventilation, the number of molecules leaving in one minute is one tenth of the molecules present at the start of that minute. How long will it take for the concentration of ammonia molecules to reach $1 \,molecule / m ^3$ ?

An archaeologist analyses the wood in a prehistoric structure and finds that ${C^{14}}$ (Half life $= 5700\, years$) to ${C^{12}} $ is only one- fourth of that found in the cells buried plants. The age of the wood is about ……..$years$