A free electron and a free proton have the same speed.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)a shorter wavelength and a smaller frequency
D)the same wavelength and a greater frequency
E)a longer wavelength and a smaller frequency

Question

Quizplus · Accepted Answer

The de Broglie wavelength formula, $\lambda = \frac{h}{mv}$, where $h$ is Planck's constant, $m$ is mass, and $v$ is velocity, shows that wavelength is inversely proportional to mass. Since the electron has a much smaller mass compared to the proton, its wavelength will be longer. Frequency ($f$) is related to wavelength ($\lambda$) and speed ($v$) by the equation $f = \frac{v}{\lambda}$. Given the same speed but a longer wavelength for the electron, its frequency will be smaller.

A Free Electron and a Free Proton Have the Same