Chapter 41 Quantum Mechanics de Broglie’s Idea Particles had wave characteristics just like waves had particle characteristics (e.g. E&M wave photon) The de Broglie wavelength of a particle of mass, m, is The frequency of matter waves is Uncertainty Principle and wave character
A non-relativistic electron and a non-relativistic proton are moving and have the same de Broglie wavelength. Which of the following are also the same for the two particles: (a) speed, (b) kinetic energy, (c) momentum, (d) frequency?
QUICK QUIZ 27.4
(c). Two particles with the same de Broglie wavelength will have the same momentum p = mv. If the electron and proton have the same momentum, they cannot have the same speed because of the difference in their masses. For the same reason, remembering that KE = p2/2m, they cannot have the same kinetic energy. Because the kinetic energy is the only type of energy an isolated particle can have, and we have argued that the particles have different energies, Equation 27.15 tells us that the particles do not have the same frequency.
QUICK QUIZ 27.4 ANSWER
We have seen two wavelengths assigned to the electron, the Compton wavelength and the de Broglie wavelength. Which is an actual physical wavelength associated with the electron: (a) the Compton wavelength, (b) the de Broglie wavelength, (c) both wavelengths, (d) neither wavelength?
QUICK QUIZ 27.5
(b). The Compton wavelength, λC = h/mec, is a combination of constants and has no relation to the motion of the electron. The de Broglie wavelength, λ= h/mev, is associated with the motion of the electron through its momentum.
QUICK QUIZ 27.5 ANSWER