Question

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. $E^{- 2}$

Answer 1

Answer: (B)

$E^{1/2}$

Answer 2

For photon $\lambda_{2} = \frac{hc}{E}$ ……. (i) and For proton

$\lambda_{1} = \frac{h}{\sqrt{2mE}}$ …….(ii)

Therefore $\frac{\lambda_{1}}{\lambda_{2}} = \frac{E^{1/2}}{\sqrt{2m}c}$ ⇒ $\frac{\lambda_{1}}{\lambda_{2}} \propto E^{1/2}$.