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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
At what temperature will the oxygen molecules have the same root mean square speed as hydrogen molecules at $200 \,K$ ....... $K$
  • A
    $800 $
  • B
    $1600 $
  • C
    $2400 $
  • ✓
    $3200 $
✓

Answer

Correct option: D.
$3200 $
d
${v_{rms}} = \sqrt {\frac{{3RT}}{M}}  \Rightarrow \,\,T \propto M$            [Since   ${v_{rms}},\,\,R \to $ constant ]         

$ \Rightarrow \,\,\,\frac{{{T_{{O_2}}}}}{{{T_{{H_2}}}}} = \frac{{{M_{{O_2}}}}}{{{M_{{H_2}}}}} \Rightarrow \,\,\frac{{{T_{{O_2}}}}}{{200}} = \frac{{32}}{2}\, \Rightarrow \,\,{T_{{O_2}}} = 3200\,K$

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