(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.

Updated on : 2022-09-05
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(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
where =Disintegration constant
For 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


(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


Dividing by volume,

Substituting the value,


Thus, these are atoms atms per unit volume in the cave.

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