Question

A photon and electron both have same energy $E_0=100eV$, then

• A. both have same wavelength
• B. photon has longer wavelength
• C. electron has longer wavelength
• D. electron has lesser momentum

Answer 1

The correct option is B photon has longer wavelength

$Wavelengthoftheelectron{\lambda }_e=\frac{h}{\sqrt{2m{E}_0}}Wavelengthofthephoton{\lambda }_p=\frac{hc}{E_0}wherehisthePlanck\text{'}scons\tan t\frac{{\lambda }_p}{{\lambda }_e}=\frac{hc}{E_0}\times \frac{\sqrt{2m{E}_0}}{h}=\frac{c}{E_0}\times \sqrt{2m{E}_0}=\sqrt{\frac{2m{c}^2}{E_0}}=\sqrt{\frac{2\times 9.1\times {10}^{-31}\times 9\times {10}^{16}}{100\times 1.6\times {10}^{-19}}}<1\Rightarrow {\lambda }_p>{\lambda }_{e}i.ethephotonhaslongerwavelengthandlessermomentum(becausep=\frac{h}{\lambda }).$