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12 . kinetic theory of gases — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics12 . kinetic theory of gases1 Mark
MCQ
Two vessels having equal volume contains molecular hydrogen at one atmosphere and helium at two atmospheres respectively. If both samples are at the same temperature, the mean velocity of hydrogen molecules is
  • A
    Equal to that of helium
  • B
    Twice that of helium
  • C
    Half that of helium
  • ✓
    $\sqrt 2 $ times that of helium
✓

Answer

Correct option: D.
$\sqrt 2 $ times that of helium
d
${v_{av}} \propto \frac{1}{{\sqrt M }}$ 

$\Rightarrow$  $\frac{{{v_{{H_2}}}}}{{{v_{He}}}} = \sqrt {\frac{{{M_{He}}}}{{{M_{{H_2}}}}}}  = \sqrt {\frac{4}{2}}  = \sqrt 2 $

 ${v_{{H_2}}} = \sqrt 2 \,{v_{He}}$

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