The de Broglie wavelength of an electron moving at 1.0×10^7 m/s is approximately what value? (m_e = 9.11×10^-31 kg)

• A. About 5.0×10^-11 m
• B. About 7.3×10^-11 m
• C. About 1.0×10^-10 m
• D. About 3.0×10^-11 m

Answer: (B)

De Broglie wavelength relates a particle’s momentum to its wave-like nature: lambda = h/p. For a nonrelativistic electron, p = mv. With mass 9.11×10^-31 kg and speed 1.0×10^7 m/s, the momentum is p = 9.11×10^-24 kg·m/s. Then lambda = h/p = (6.626×10^-34 J·s) / (9.11×10^-24 kg·m/s) ≈ 7.3×10^-11 m. Since the speed is well below light speed, using p = mv is appropriate and gives a wavelength of about 7×10^-11 m, matching the listed value.