Q: 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

(A) E^{0}

(B) E^{1/2}

(C) E^{–1}

(D) E^{–2}

Ans: (B)

Sol: $\large \frac{\lambda_1}{\lambda_2} = \frac{ \frac{h}{\sqrt{2mE}}}{ \frac{hc}{E}}$

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