Find random number of molecules in a particular cube of air

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Reference no: EM131810330

Question: Regard the positions of molecules I a room as the points of a Poisson random scatter in 3 dimensions. According to physics. There are about 6.023x1023 molecules in every 22.4 liters of air at normal temperature and pressure. (A liter is 1000 cubic centimeters.) Let N(x) be the random number of molecules in a particular cube of air with sides of length x centimeters.

a) Calculate the mean µ(x) and standard deviation σ(x) of N(x).

b) How small does x have to in order that σ(x) be 1% of µ(x). so fluctuations in density of around 1% over a cube of length x are likely to occur?

Reference no: EM131810330

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