  Question

# (a) Plot a graph showing the variation of undecayed nuclei versus time . From the graph, find out how one can determine the half-life and average life of the radioactive nuclei.(b) The air in some caves includes a significant amount of radon gas, which can lead to lung cancer if breathed over a prolonged time. In British caves, the air in the cave with the greatest amount of the gas has an activity per volume of . Suppose that you spend two full days exploring (and sleeping in) that cave. Approximately how many atoms would you take in and out of your lungs during your two-day stay? The radionuclide in radon gas has a half-life of 3.82 days. You need to estimate your lung capacity and average breathing rate.

Hard
Updated on : 2022-09-05
Solution Verified by Toppr

## (a) Law of Radioactivity defines that the number of Nuclei undergoing number of Nuclei present in the sample at that Instant.Since from the graph; we have         ....1where =Disintegration constantFor For is the time at =  And for Mean life -we have to sum it over the whole Range for for number of nuclei which decay in time t to t  t ;  For Integration it over the Range = Mean-life (b) The equation for the activity is given by: Here, R is the activity, N is the number of nuclei and is the decay constant. The equation for the decay constant is given by,  Here, is the half - life Thus, Dividing by volume, Substituting the value,               Thus, these are atoms atms per unit volume in the cave.   0 0