Question

An ideal gas is under standard conditions. Find the diameter of the sphere within whose volume the relative fluctuation of the number of molecules is equal to  η = 1.0.10^-3. What is the average number of molecules inside such a sphere?

Answer 1

In a sphere of diameter d there are

where n₀  = Loschmidt's number = No. of molecules per unit volume (1 cc) under NTP.

The relative fluctuation in this umber is 

The average number of molecules in this sphere is 1/η² = 10⁶