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

Question

Quizplus · Accepted Answer

The de Broglie wavelength of a particle is given by λ = h/p, where h is Planck's constant and p is the momentum of the particle. Since kinetic energy (KE) is given by KE = p^2/(2m) (where m is the mass of the particle), for the same kinetic energy, a particle with a smaller mass (like an electron compared to a proton) will have a larger momentum. This results in the electron having a shorter de Broglie wavelength than the proton. However, the frequency of the matter wave is related to the particle's energy, not its momentum directly. Since they have the same kinetic energy, the frequency of their matter waves would be the same. Therefore, the correct answer is that the electron's matter wave has a longer wavelength and the same frequency compared to the proton's matter wave.

A Free Electron and a Free Proton Have the Same