question_answer

An electron and a proton have the same de-Broglie wavelength. Which one of these has higher kinetic energy? Which one is moving faster?

Answer:

                de-Broglie wavelength of a particle of mass m and kinetic energy K is      \[\lambda =\frac{h}{\sqrt{2mK}}\]                 or            \[{{\lambda }^{2}}=\frac{{{h}^{2}}}{2mK}\]                 \[\therefore \]  \[K=\frac{{{h}^{2}}}{2m{{\lambda }^{2}}}\] For particles having same\[\lambda ,K\propto \frac{1}{m}\] As the mass of electron is smaller than that of proton, so the electron has a higher kinetic energy and it is moving faster.