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For a molecule of an ideal gas n=3×108cm3 and mean free path is 10-2cm. Calculate the diameter of the molecule

a
2.7×10−4cm
b
3.7×10−4cm
c
4.7×10−4cm
d
6.7×10−4cm

detailed solution

Correct option is A

Given number of molecules per unit volume is n=3×108cm−1,mean free path is λ=10−2cm; diameter of molecule is dλ=12πnd2d2=12πnλd2=12×3.14×3×108×10−2d2=10−61.414×3.14×3d=7.5×10−8=7.5×10−4d=2.7×10−4cm Hence the diameter of the molecule of the gas is 2.7×10−4cm

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