- Home
- Standard 11
- Physics
$27°C$ તાપમાને અને $1 \,atm$ દબાણે હાઈડ્રોજન અને ઑક્સિજનના અણુઓ માટે ($\nu_{rms}$) / ($\nu_{rms}$) = .. .....
$1/4$
$16$
$1/16$
$4$
Solution
અહી $ {m_{{O_2}}} = 32\,g\,{(mol)^{ – 1}},\,\,\,{m_{{H_2}}}\, = \,2\,g\,{(mol)^{ – 1}},\,\,\,\,$
${\upsilon _{rms}}\, = \,\sqrt {\frac{{3\,\,{k_B}T}}{m}} $ પરથી ${({\upsilon _{rms}})_{{O_2}}} \propto \frac{1}{{\sqrt {{m_{{O_2}}}} }}\,\,\,…\,\,\,…\,\,\,…\,\,(1)\,\,\,\,\,$
${({\upsilon _{rms}})_{{H_2}}} \propto \frac{1}{{\sqrt {{m_{{H_2}}}} }}\,\,\,…\,\,\,…\,\,\,…\,\,(2)$
$\therefore \frac{{\,{{({\upsilon _{rms}})}_{{H_2}}}}}{{{{({\upsilon _{rms}})}_{{O_2}}}}}\,\, = \,\,\sqrt {\frac{{{m_{{O_2}}}}}{{{m_{{H_2}}}}}} = \sqrt {\frac{{32}}{2}} \,\, = \,\,4\,\,\,\,\,\,\therefore \,\frac{{\,{{({\upsilon _{rms}})}_{{H_2}}}}}{{{{({\upsilon _{rms}})}_{{O_2}}}}}\,\, = 4$
