The mediator here, the photon, is a virtual particle and as such exists for an amount of time allowed by the Hesenberg Uncertainty Principle. Therefore the photon must satisfy, [tex]ΔE Δt ≥\hbar[/tex]
To find this [itex]ΔE[/itex] requires knowledge of [itex]Δt[/itex], which could be found using the distance between the electrons divided by the speed of light. Then use the above equation to solve for [itex]ΔE[/itex], from which [itex]λ[/itex] can be found using [tex]ΔE = \frac{hc}{λ}[/tex]