Electrostatic force between 3 molecules?

Because of the symmetry, the free electron is equidistant from both sodium and chloride ion, by Pythagorean theorem the distance is

r = √( (0.120 nm)² + (0.439 nm)² ) = 0.455 nm = 0.455 x 10^-9 m.

Chloride ion has a negative elementary charge e = 1.602 x 10^-19 C (one electron extra) and sodium ion a positive elementary charge (one proton extra).

We use Coulomb's law for the magnitude of the electrostatic force between a free electron and one of the ions - it is equal because of the same distance and both of the charges:

F = k x e x e / r² = 8.99 x 10^9 N m² / C² x (1.602 x 10^-19 C)² / (0.455 x 10^-9 m)² = 1.11 x 10^-9 N.

The force between sodium ion and the free electron is attractive (one charge positive, another negative), while another is repulsive (both charges are negative).

Because of the symmetry, the vertical components of these two forces are equal and opposite, so they cancel out; hence a total force is horizontal and equals

Fo = F x cos θ + F x cos θ = 2F cos θ, where θ is the angle between lines ions-free electron and cos θ = 0.120 nm / 0.455 nm = 0.2637 and Fo = 2 x 1.11 x 10^-9 N x 0.2637 = 5.85 x 10^-10 N. The force is paralel to a molecule and points toward sodium ion.

i think of this may well be a trick question, the hydrogen molecule ion has basically one electron! "The hydrogen molecule ion H+2 is the only molecule for which we are able to clean up the digital Schrödinger equation precisely with the aid of fact it basically has one electron." -Mark E. Tuckerman