An engineer investigating a new refrigerant measures its density in the liquid phase to be ${\rho }_L=1200{kg\; m}^{-3}$, and in its gaseous phase to be ${\rho }_G=1.2{kg\; m}^{-3}$.

Using a simplified cubic particle model where each molecule of mass $m$ occupies a volume of $d^3$ (where $d$ is the mean molecular spacing), estimate the ratio of the mean molecular spacing in the gas to that in the liquid, $\frac{d_G}{d_L}$.