De Broglie Wavelength
Wavelength associated with a moving particle
Formula
λ = h / p
p = m v
- λ = wavelength (m)
- h = Planck constant (6.626 × 10â»Â³â´ J·s)
- p = momentum (kg·m/s)
- m = mass (kg)
- v = velocity (m/s)
Example
Given: electron, m = 9.109 × 10â»Â³Â¹ kg, v = 1.0 × 10ⶠm/s.
p = (9.109 × 10â»Â³Â¹) × (1.0 × 10â¶) = 9.109 × 10â»Â²âµ kg·m/s
λ = (6.626 × 10â»Â³â´) / (9.109 × 10â»Â²âµ) ≈ 7.27 × 10â»Â¹â° m = 0.727 nm
Answer: λ ≈ 0.727 nm
Common Mistakes
Unit conversion errors
Keep SI units: mass in kg, velocity in m/s, wavelength in m.
Using energy instead of momentum
For KE given, compute v first, then p = mv.
FAQ
Does this apply to macroscopic objects?
Yes, but wavelength is immeasurably small for large masses.
What if relativistic speeds?
Use relativistic momentum p = γ m v where γ = 1/√(1 - v²/c²).