• # question_answer At constant volume and temperature conditions, the rate of diffusion ${{D}_{A}}$ and ${{D}_{B}}$ of gases A and B having densities ${{\rho }_{A}}$ and ${{\rho }_{B}}$ are related by the expression      [IIT 1993] A)                 ${{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}$     B)                 ${{D}_{A}}={{\left[ {{D}_{B}}\cdot \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right]}^{1/2}}$ C)                 ${{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{A}}}{{{\rho }_{B}}} \right)}^{1/2}}$ D)                 ${{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{1/2}}$

$\frac{{{D}_{A}}}{{{D}_{B}}}=\sqrt{\frac{{{\rho }_{B}}}{{{\rho }_{A}}}}={{\left[ \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right]}^{\frac{1}{2}}}$;  $\therefore {{D}_{A}}={{D}_{B}}{{\left( \frac{{{\rho }_{B}}}{{{\rho }_{A}}} \right)}^{\frac{1}{2}}}$