Some laboratory furnace have small glass windows so that samples may be observed

Question

Some laboratory furnace have small glass windows so that samples may be observed. One problem associated with such windows is gas leakage. Suppose that a furnace has a 3%u2010mm thick window of silicate glass, and that the furnace contains helium. If the cross%u2010sectional area of the window is 600 mm2, calculate the number of atoms of helium gas that flow across the window in 1 hour. The concentration of helium in the furnace 6.0 x 1023 atoms/m3 and outside it is zero. The diffusion coefficient for helium in silicate glass at the furnace temperature is 1.0 x 10%u201010 m2/s.

My answer: 4.32*10^18 atoms but I dont think this is right...

I did -(1.0*10^-10 m^2/s)(6.022*10^23 atoms/m^3/3*10^-3m)(2*10^16 atoms/m^2*s)(3600 s/hr)(600 mm^2)(0.0001 m^2/1mm^2)

I just am not sure whether to use steady state diffusion or non-steady state diffusion. Please help explain to me what I'm messing up thank you!

Explanation / Answer

It is 10^-6 m^2/1mm^2 not 0.0001.

so it is -(1.0*10^-10 m^2/s)(6.022*10^23 atoms/m^3/3*10^-3m)(3600 s/hr)(600 mm^2)(0.0001 m^2/1mm^2) = 4.32*10^16 atoms

its an unit conversion mistake.

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