A 1.0 kg object moves at 1.0 m/s. What is its de Broglie wavelength?

A 1.0 kg object moves at 1.0 m/s. What is its de Broglie wavelength?

• A. 6.63×10^-25 m
• B. 6.63×10^-34 m
• C. 6.63×10^-20 m
• D. 6.63×10^-40 m

Answer: (B)

The main idea is that a particle’s wave-like nature is described by the de Broglie relation, where the wavelength is the Planck constant divided by the momentum: λ = h/p. For this object, momentum p = m v = 1.0 kg × 1.0 m/s = 1.0 kg·m/s. Using h ≈ 6.63 × 10^-34 J·s, the wavelength is λ ≈ (6.63 × 10^-34) / (1.0) = 6.63 × 10^-34 meters. This matches the small, 10^-34 m scale expected for macroscopic masses moving at modest speeds. The other options differ by many powers of ten, which would correspond to much different momenta and aren’t consistent with the given mass and speed.

The main idea is that a particle’s wave-like nature is described by the de Broglie relation, where the wavelength is the Planck constant divided by the momentum: λ = h/p. For this object, momentum p = m v = 1.0 kg × 1.0 m/s = 1.0 kg·m/s. Using h ≈ 6.63 × 10^-34 J·s, the wavelength is λ ≈ (6.63 × 10^-34) / (1.0) = 6.63 × 10^-34 meters. This matches the small, 10^-34 m scale expected for macroscopic masses moving at modest speeds. The other options differ by many powers of ten, which would correspond to much different momenta and aren’t consistent with the given mass and speed.