The potential energy of gas molecules in a certain central field depends on the distance r from the field's centre as U(r) = ar^2 , where a is a positive constant. The gas temperature is T, the concentration of molecules at the centre of the field is n0 . Find: (a) the number of molecules located at the distances between r and r + dr from the centre of the field; (b) the most probable distance separating the molecules from the centre of the field; (c) the fraction of molecules located in the spherical layer between r and r + dr; (d) how many times the concentration of molecules in the centre of the field will change if the temperature decreases n times.
Solution:
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