In electron diffraction, an electron moving at speed v

Question

In electron diffraction, an electron moving at speed v << c acts like
A) a particle with momentum mv.
B) a particle with position coordinate v/t.
C) a wave with wavelength v/t.
D) a wave with wavelength h/mv.
E) both a particle with position coordinate v/t and a wave with wavelength v/t.

Quizplus · Accepted Answer

According to de Broglie's wavelength equation for matter waves, the wavelength of an electron with momentum p is given by λ = h/p. For an electron with speed v, the momentum is given by p = mv/sqrt(1 - v^2/c^2), where c is the speed of light. For v << c, we can neglect the denominator and write p ≈ mv. Substituting this in the de Broglie wavelength equation, we get λ = h/mv. Therefore, an electron in electron diffraction behaves like a wave with wavelength h/mv.

In Electron Diffraction, an Electron Moving at Speed V