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Physics Question on kinetic theory

A bulb contains one mole of hydrogen mixed with one mole of oxygen at temperature TT. The ratio of r.m.s.r.m.s. values of velocity of hydrogen molecules to that of oxygen molecules, is

A

4:01

B

1:16

C

1:04

D

16:01

Answer

4:01

Explanation

Solution

Given: One mole of hydrogen mixed with one mole of oxygen. We know that r.m.s. velocity (vrms)=3RTMμ1M\left(v_{rms}\right)=\sqrt{\frac{3RT}{M}}\mu \sqrt{\frac{1}{M}} or (vrms)H(vrms)O=MOMH=322=41.\frac{\left(v_{rms}\right)_{H}}{\left(v_{rms}\right)_{O}}=\sqrt{\frac{M_{O}}{M_{H}}}=\sqrt{\frac{32}{2}}=\frac{4}{1}. or (vrms)H:(vrms)O=4:1.\left(v_{rms}\right)_{H} : \left(v_{rms}\right)_{_O}= 4 : 1.