Question

If m is the mass of an electron and c is the speed of light, the ratio of the wavelength of a photon of energy E to that of the electron of the same energy is

• A. $ c\sqrt{\frac{2m}{E}} $
• B. $ \sqrt{\frac{2m}{E}} $
• C. $ \sqrt{\frac{2m}{cE}} $
• D. $ \sqrt{\frac{m}{E}} $
• E. $ \sqrt{\frac{cm}{E}} $

Answer 1

Answer: (A)

Energy, $ E=\frac{hc}{{{\lambda }_{p}}} $
or $ {{\lambda }_{p}}=\frac{hc}{E} $ and $ {{\lambda }_{e}}=\frac{h}{p}=\frac{hc}{\sqrt{2mE}} $
$ \therefore $ $ \frac{{{\lambda }_{p}}}{{{\lambda }_{e}}}=\frac{E}{\frac{h}{\sqrt{2mE}}} $
or $ \frac{{{\lambda }_{p}}}{{{\lambda }_{e}}}=\frac{c\sqrt{2mE}}{E}=c\sqrt{\frac{2m}{E}} $