Question 28.Q-Q.5: An electron and a proton both moving at nonrelativistic spee...
An electron and a proton both moving at nonrelativistic speeds 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
(c). According to Equation 28.10, two particles with the same de Broglie wavelength have the same momentum p = mv. If the electron and proton have the same momentum, they cannot have the same speed (a) because of the difference in their masses. For the same reason, remembering that K=p^{2} / 2 m , they cannot have the same kinetic energy (b). Because the particles have different kinetic energies, Equation 28.11 tells us that the particles do not have the same frequency (d).
\lambda=\frac{h}{p}=\frac{h}{m v} [28.10]
f=\frac{E}{h} [28.11]