QNT-02

de Broglie wavelength

λ = h / p = h / (m v).

Reading speed

Wave–particlede Broglie 1924

Governing equation

\lambda=\dfrac{h}{p}=\dfrac{h}{mv}

where

m: Mass (u)
v: Speed (m/s)
\lambda: Wavelength (pm)

Lecture brief

Historical brief

Planck (1900), Einstein’s photoelectric law, Bohr, de Broglie, Heisenberg and Schrödinger’s 1926 equation rebuilt matter as amplitude. These sheets are the first solvable models: wells, spin, tunneling, uncertainty. This sheet (QNT-02 — de Broglie wavelength) is the form associated with de Broglie 1924. Working symbols: $m$ , $v$ $\rightarrow$ $\lambda$ . de Broglie assigned every particle a wavelength h/p, later confirmed by Davisson–Germer electron diffraction.

Purpose

Purpose: compute

\lambda

from

m

v

in Quantum mechanics via

\lambda=\dfrac{h}{p}=\dfrac{h}{mv}

λ = h / p = h / (m v). Use it when a real quantum mechanics question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

m = 1.000\,\mathrm{u}

v = 1000.000\,\mathrm{m/s}

, the governing relation

\lambda=\dfrac{h}{p}=\dfrac{h}{mv}

yields

\lambda = 399.0313\,\mathrm{pm}

. Non-relativistic particle. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Mass m1 uSpeed v1000 m/s

Outputs

Wavelength \lambda399.0313 pm

Reading speed

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Narration of this film

Non-relativistic particle.

de Broglie assigned every particle a wavelength h/p, later confirmed by Davisson–Germer electron diffraction.

Reading speed

Watch on YouTube