Matter waves: 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, $\lambda = \frac{h}{p}$, where $h$ is Planck's constant and $p$ is momentum, implies that if two particles have the same wavelength, they must have the same momentum, making choice C correct. Since kinetic energy ($KE$) is given by $\frac{p^2}{2m}$ (where $p$ is momentum and $m$ is mass), and the electron has a much smaller mass than the proton, for the same momentum, the electron's kinetic energy must be higher, making choice D correct. Choices A, B, and E are incorrect because they do not align with the principles of quantum mechanics and the relationships between momentum, mass, and kinetic energy.

Matter Waves: a Nonrelativistic Electron and a Nonrelativistic Proton Have