A free electron and a free proton have the same momentum.This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has:
A)a shorter wavelength and a greater frequency
B)a longer wavelength and a greater frequency
C)the same wavelength and the same frequency
D)the same wavelength and a greater frequency
E)the same wavelength and a smaller frequency

Question

Quizplus · Accepted Answer

The de Broglie wavelength formula, $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is momentum, shows that if two particles have the same momentum, they will have the same wavelength ($\lambda$). However, because the electron is lighter than the proton, for the same momentum, its velocity must be higher. Since frequency ($f$) is related to velocity ($v$) and wavelength ($\lambda$) by the equation $f = \frac{v}{\lambda}$, and both particles have the same $\lambda$ but the electron moves faster, the electron will have a greater frequency.

A Free Electron and a Free Proton Have the Same