The Van Der Waals Forces in Gases

Abstract

A calculation of van der Waal's potential of two atoms at large separation has been carried out for hydrogen and helium. The method depends upon a representation of the perturbed wave function of the system as $\psi ={\psi }_0 \mathrm{}(1+vR)\mathrm{}$ where ${\psi }_0$ is the unperturbed wave function, $v$ the perturbing potential and $R$ is a function of the radial coordinates of the electrons. The method is equally well adapted to the calculation of polarizabilities. A computation of the mutual energy of two hydrogen atoms confirms the results of Eisenschitz and London. The polarizability of helium is calculated as 0.210×${10}^{-24\mathrm{}}$ cc which agrees well with the experimental value, 0.205×${10}^{-24\mathrm{}}$. The mutual energy of two helium atoms is found to be -3.18 $\frac{E_0}{{\left(\frac{R}{a_0}\right)}^6}$. A correlation between the mutual energy of the two molecules, $\epsilon$, and the polarizability, $\alpha$, is obtained: $\epsilon =\frac{-1.36\mathrm{}{{\nu }_0}^{\frac{1}{2}}{a_0}^{\frac{3}{2}}{a}^{\frac{3}{2}}{E}_0}{R^6}$ where ${\nu }_0$ is the number of electrons in the highest quantum state in the molecule, $E_0$ the energy of the hydrogen atom in the normal state, and $R$ is the separation of the molecules. By means of this formula, the van der Waals cohesive pressure constant is calculated for Ne, A, ${\mathrm{N}}_2$, ${\mathrm{H}}_2$, ${\mathrm{O}}_2$, and C${\mathrm{H}}_4$.