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 ${\lambda }_1/{\lambda }_2$ is proportional to

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

Answer 1

The correct option is B $E^{1/2}$

For photon ${\lambda }_2=\frac{hc}{E}$ ......(i) and For proton ${\lambda }_1=\frac{h}{\sqrt{2mE}}$ ......(ii) Therefore $\frac{{\lambda }_1}{{\lambda }_2}=\frac{E^{1/2}}{\sqrt{2m}c}\Rightarrow \frac{{\lambda }_1}{{\lambda }_2}\propto E^{1/2}$.