The kinetic energy of a proton is equal to the energy $E$ of a photon. If ${\lambda }_1$ be the (de-Broglie) wavelength of the proton and ${\lambda }_2$ that of the proton, then the ratio $\frac{{\lambda }_1}{{\lambda }_2}$ is proportional to:

Light of wavelength $\lambda$ falls on a cathode plate inside a vacuum tube as shown in the figure. The work function of the cathode surface is $W$ and the anode is a wire mesh of conducting material kept at a distance $d$ from the cathode. A potential difference $V$ is maintained between the electrodes. If the minimum de-Broglie wavelength of the electrons passing through the anode is ${\lambda }_e$, which of the following statement is true?