QNT-13

Planck relation

E = h f = ħ ω. A quantum of an oscillator of frequency f.

Reading speed

QuantaPlanck

Governing equation

E=hf=\hbar\omega

$f \in \left[1\times 10^{12}, 1\times 10^{16}\right]$

where

f: Frequency (Hz)
E: Photon energy (eV)

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

E=hf=\hbar\omega

$f \in \left[1\times 10^{12}, 1\times 10^{16}\right]$

$f = 1\times 10^{12}$ $E = 0.004$

Along the curve

②

Domain of the variable — blue

f_{\min} = 1\times 10^{12},\quad f_{\max} = 1\times 10^{16}

$f \in \left[1\times 10^{12}, 1\times 10^{16}\right]$

$f = 1\times 10^{12}$ $f = 1\times 10^{12}$

Along the curve

③

Response curve — green

E=hf=\hbar\omega

$f \in \left[1\times 10^{12}, 1\times 10^{16}\right]$

$f = 1\times 10^{12}$ $E = 0.004$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}f}

$f \in \left[1\times 10^{12}, 1\times 10^{16}\right]$

$f = 6.39\times 10^{13}$ $E^{\prime} = 4.14\times 10^{-15}$

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-13 — Planck relation) is the form associated with Planck. Working symbols: $f$ $\rightarrow$ $E$ . The ultraviolet catastrophe dies when energy is counted in packets hf.

Purpose

Purpose: compute

E

from

f

in Quantum mechanics via

E=hf=\hbar\omega

E = h f = ħ ω. A quantum of an oscillator of frequency f. 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

f = 5.000e+14\,\mathrm{Hz}

, the governing relation

E=hf=\hbar\omega

yields

E = 2.068\,\mathrm{eV}

. A spectrum, rungs of hf, a fading tail. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f500000000000000 Hz

Outputs

Photon energy E2.068 eV

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A spectrum, rungs of hf, a fading tail.

The ultraviolet catastrophe dies when energy is counted in packets hf.

Reading speed

Watch on YouTube