The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let λ₁ be the de-Broglie wavelength of the proton and  λ₂ be the wavelength of the photon. The ratio λ₁ /λ₂ is proportional to

E^1/2

Energy of proton = Energy of photon

 Wavelength of  PROTON is  $ \lambda_1 = \frac{h}{p} = \frac{h}{\sqrt {2mE}}\propto \frac{1}{\sqrt E}$

Wavelength of a PHOTON is $\lambda_2 = \frac{hc}{E} \propto \frac{1}{E}$

$\Rightarrow \frac{\lambda_1}{\lambda_2} \propto E^{\frac{1}{2}}$