Kinetic Theory

JEE Main level, single correct, medium

57 of 168

Question 57 of 168

Two gases - argon (atomic radius 0.07nm,0.07nm, atomic weight 4040 ) and xenon (atomic radius 0.1nm,0.1nm, atomic weight 140140 ) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to:

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Answer: (B) 1.831.83

Mean free time =12nπd2vrms=\dfrac{1}{\sqrt{2}n\pi {d}^{2}{v}_{rms}}
tArtXe=dXe2dAr2×m1m2\dfrac{{t}_{Ar}}{{t}_{Xe}}=\dfrac{{d}_{Xe}^{2}}{{d}_{Ar}^{2}}\times \sqrt{\dfrac{{m}_{1}}{{m}_{2}}}
=(0.10.07)2×40140={\left(\dfrac{0.1}{0.07}\right)}^{2}\times \sqrt{\dfrac{40}{140}}
=(107)2×27=1.09={\left(\dfrac{10}{7}\right)}^{2}\times \sqrt{\dfrac{2}{7}}=1.09
closest value is 1.831.83

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