Answer
The electron should be accelerated from rest through the potential difference $\frac{V_{\circ}}{4}$.
Work Step by Step
We know that $\lambda=\frac{h}{p}$. This equation shows that if the wavelength is doubled then the momentum is halved. We also know that $K=\frac{p^2}{2m}$; according to this equation, the kinetic energy decreases by a factor of four. We conclude that the electron should be accelerated from rest through the potential difference $\frac{V_{\circ}}{4}$.
