The potential energy of gas molecules in a certain central field depends on the distance r from the field's centre as U (r) = ar2, where a is a positive constant. The gas temperature is T, the concentration of molecules at the centre of the field is no. 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 η times.