Two modern-physics results in one tool: the de Broglie wavelength of a particle from its mass and velocity, and the energy of a photon from its wavelength.
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Question: Find the de Broglie wavelength of an electron moving at 1.0 × 10⁶ m s⁻¹.
Step 1 — momentum.
p = m v = (9.109 × 10⁻³¹ kg)(1.0 × 10⁶ m s⁻¹) = 9.109 × 10⁻²⁵ kg·m·s⁻¹
Step 2 — wavelength.
λ = h / p = (6.626 × 10⁻³⁴) / (9.109 × 10⁻²⁵)
Divide the numbers: 6.626 ÷ 9.109 = 0.7274. Subtract the powers: 10⁻³⁴ ÷ 10⁻²⁵ = 10⁻⁹.
λ = 0.7274 × 10⁻⁹ = 7.27 × 10⁻¹⁰ m = 0.727 nm = 7.27 Å
Why this number matters: atoms in a crystal are spaced a few times 10⁻¹⁰ m apart, the same size as this wavelength — so a crystal can act as a diffraction grating for the electron.
Worked in full in de Broglie Wavelength — Matter Waves Calculated.
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