Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their…

Given, $\frac{{\text{m}}_{\text{A}}}{{\text{m}}_{\text{B}}}=\frac{2}{\mathrm{3\; }}$
$\because$ Volume and temperature is same.
From ideal gas equation, $PV=nRT$
$\frac{\text{P}}{\text{n}} = constant$
$\frac{{\text{P}}_{\text{A}}}{{\text{n}}_{\text{A}}}=\frac{{\text{P}}_{\text{B}}}{{\text{n}}_{\text{B}}}\Rightarrow \frac{{\text{n}}_{\text{A}}}{{\text{n}}_{\text{B}}}=\frac{{\text{P}}_{\text{A}}}{{\text{P}}_{\text{B}}}=\frac{4}{3}$

Also, density, $\rho =\frac{M}{V}$
$\frac{{\text{ρ}}_{\text{A}}}{{\text{ρ}}_{\text{B}}}=\frac{{\text{M}}_{\text{A}}/\mathit{\text{v}}}{{\text{M}}_{\text{B}}/\mathit{\text{v}}}=\frac{{\text{n}}_{\text{A}}{m}_{\text{A}}}{{\text{n}}_{\text{B}}{\text{m}}_{\text{B}}}$
      $=\frac{4}{3}\times \frac{2}{3}=\frac{8}{9}$.