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}

$v \in \left[1, 1\times 10^{7}\right]$

where

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

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

00:0 / 00:08

①

Governing law — red

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

$v \in \left[1, 1\times 10^{7}\right]$

$v = 1$ $\lambda = 3.99\times 10^{5}$

Along the curve

②

Domain of the variable — blue

v_{\min} = 1,\quad v_{\max} = 1\times 10^{7}

$v \in \left[1, 1\times 10^{7}\right]$

$v = 1$ $v = 1$

Along the curve

③

Response curve — green

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

$v \in \left[1, 1\times 10^{7}\right]$

$v = 1$ $\lambda = 3.99\times 10^{5}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\lambda}{\mathrm{d}v}

$v \in \left[1, 1\times 10^{7}\right]$

$v = 62894.1$ $\lambda^{\prime} = -3.172$

Along the curve

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

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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