A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength.Which of the following statements about these particles are accurate? (There may be more than one correct choice.)
A) Both particles have the same speed.
B) Both particles have the same kinetic energy.
C) Both particles have the same momentum.
D) The electron has more kinetic energy than the proton.
E) The electron has more momentum than the proton.

Question

Quizplus · Accepted Answer

The de Broglie wavelength formula is λ = h/p, where λ is the wavelength, h is Planck's constant, and p is the momentum. If two particles have the same de Broglie wavelength, they must have the same momentum, making choice C correct. For nonrelativistic particles, kinetic energy (KE) is given by KE = p^2/2m, where p is momentum and m is mass. Since the electron has a much smaller mass than the proton, for the same momentum, the electron will have more kinetic energy, making choice D correct.

A Nonrelativistic Electron and a Nonrelativistic Proton Have the Same