Question

The energy of a photon is equal to the kinetic energy of a proton. The energy of the photon is E. Let $\lambda_1$ be the de-Broglie wavelength of the proton and $\lambda_2$ be the wavelength of the photon. The ratio $\frac{\lambda_1}{\lambda_2}$ is proportional to

• A. $E^0$
• B. $E^{\frac{1}{2}}$
• C. $E^{-1}$
• D. $E^{-2}$

Answer 1

Answer: (B)

$E^{\frac{1}{2}}$

Answer 2

$\frac{\lambda_1}{\lambda_2} = \frac{\frac{h}{\sqrt2mE}}{\frac{hc}{E}} \, \, or\, \, \frac{\lambda_1}{\lambda_2} ? E^{1/2}$ Therefore, the correct option is (b)