de Broglie Matter Waves

Louis de Broglie proposed that every moving object has a wavelength, not just light. A fast, heavy object has an incredibly tiny wavelength, but a light, slow particle like an electron has a wavelength large enough to make it diffract — bend and interfere — just like a wave passing through a crystal.

λ = h / p

• λ — wavelength (m): the matter wave's length associated with the moving object
• h — Planck's constant (J·s): a tiny fixed number, about 6.63 × 10⁻³⁴ joule-seconds
• p — momentum (kg·m/s): mass times velocity — how much motion the object carries

An electron has a momentum of 6.63 times ten to the minus twenty-four kilogram meters per second. What is its de Broglie wavelength?

• h = 6.63 × 10⁻³⁴ J·s
• p = 6.63 × 10⁻²⁴ kg·m/s

1. λ = h / p
2. λ = (6.63 × 10⁻³⁴ J·s) / (6.63 × 10⁻²⁴ kg·m/s)

λ = 1 × 10⁻¹⁰ m

If the electron's momentum doubles to 1.326 × 10⁻²³ kilogram meters per second, what happens to its wavelength?

• It halves to 5 × 10⁻¹¹ m
• It doubles to 2 × 10⁻¹⁰ m
• It stays at 1 × 10⁻¹⁰ m

A thrown baseball also has a de Broglie wavelength. Why can't we ever see it diffract like the electron does?

• Baseballs don't actually have a wavelength
• Its wavelength is far too small to detect
• Baseballs move too slowly to have momentum