An electron moving with speed $\mathrm{v}$ and a photon moving with speed c, have same D-Broglie wavelength. The ratio of kinetic energy of electron to that of photon is:
Correct Option: , 3
$\lambda_{\mathrm{e}}=\lambda_{\mathrm{Ph}}$
$\frac{\mathrm{h}}{\mathrm{p}_{\mathrm{e}}}=\frac{\mathrm{h}}{\mathrm{p}_{\mathrm{ph}}}$
$\sqrt{2 \mathrm{mk}_{\mathrm{e}}}=\frac{\mathrm{E}_{\mathrm{ph}}}{\mathrm{c}}$
$2 \mathrm{mk}_{\mathrm{e}}=\frac{\left(\mathrm{E}_{\mathrm{ph}}\right)^{2}}{\mathrm{c}^{2}}$
$\frac{\mathrm{k}_{\mathrm{e}}}{\mathrm{E}_{\mathrm{ph}}}=\frac{\mathrm{E}_{\mathrm{ph}}}{\mathrm{c}^{2}}\left(\frac{1}{2 \mathrm{~m}}\right)$
$=\frac{\mathrm{p}_{\mathrm{ph}}}{\mathrm{c}}\left(\frac{1}{2 \mathrm{~m}}\right)$
$=\frac{\mathrm{p}_{\mathrm{e}}}{\mathrm{c}}\left(\frac{1}{2 \mathrm{~m}}\right)$
$=\frac{\mathrm{mv}}{\mathrm{c}} \frac{1}{2 \mathrm{~m}}$
$=\frac{\mathrm{v}}{2 \mathrm{c}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.