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
Answer & explanation
Correct answer: option 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 $\lambda_2 = \frac{hc}{E} \propto \frac{1}{E}$
$\Rightarrow \frac{\lambda_1}{\lambda_2} \propto E^{\frac{1}{2}}$