If $m$ is the mass of an electron and $c$ is the speed of light, the ratio of the wavelength of a ph

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\

Professor PC Thomas Classes · Answer

Energy of photo, $\mathrm{E}=\mathrm{h} v=\frac{\mathrm{hc}}{\lambda_{\mathrm{ph}}}$ Where $\lambda_{\mathrm{ph}}$ is the wavelength of a photon\ $\lambda_{\mathrm{ph}}=\frac{\mathrm{hc}}{\mathrm{E}}$\ Wavelength of the electron, $\lambda_{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mE}}}$\ $	herefore \frac{\lambda_{\mathrm{ph}}}{\lambda_{\mathrm{e}}}=\frac{\mathrm{hc}}{\mathrm{E}} 	imes \frac{\sqrt{2 \mathrm{mE}}}{\mathrm{h}}=\mathrm{c} \sqrt{\frac{2 \mathrm{~m}}{\mathrm{E}}}$\