QNT-08

Planck–Einstein relation

E = h f = h c / λ.

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PhotonsPlanck 1900

Governing equation

E=hf=\dfrac{hc}{\lambda}

$\lambda \in \left[0.01, 2000\right]$

where

\lambda: Wavelength (nm)
E: Photon energy (eV)
f: Frequency (THz)

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.

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①

Governing law — red

E=hf=\dfrac{hc}{\lambda}

$\lambda \in \left[0.01, 2000\right]$

$\lambda = 0.01$ $E = 1.24\times 10^{5}$

Along the curve

②

Domain of the variable — blue

\lambda_{\min} = 0.01,\quad \lambda_{\max} = 2000

$\lambda \in \left[0.01, 2000\right]$

$\lambda = 0.01$ $\lambda = 0.01$

Along the curve

③

Response curve — green

E=hf=\dfrac{hc}{\lambda}

$\lambda \in \left[0.01, 2000\right]$

$\lambda = 0.01$ $E = 1.24\times 10^{5}$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}E}{\mathrm{d}\lambda}

$\lambda \in \left[0.01, 2000\right]$

$\lambda = 12.59$ $E^{\prime} = -4926.4$

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-08 — Planck–Einstein relation) is the form associated with Planck 1900. Working symbols: $\lambda$ $\rightarrow$ $E$ , $f$ . Planck introduced E = h f to quantise cavity oscillators; Einstein applied it to the free electromagnetic field as photons.

Purpose

Purpose: compute

E

f

from

\lambda

in Quantum mechanics via

E=hf=\dfrac{hc}{\lambda}

E = h f = h c / λ. 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

\lambda = 500.000\,\mathrm{nm}

, the governing relation

E=hf=\dfrac{hc}{\lambda}

yields

E = 2.4797\,\mathrm{eV}

f = 599.585\,\mathrm{THz}

. Monochromatic photon. Enter λ in nm. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Wavelength \lambda500 nm

Outputs

Photon energy E2.4797 eV
Frequency f599.585 THz

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Narration of this film

Monochromatic photon. Enter λ in nm.

Planck introduced E = h f to quantise cavity oscillators; Einstein applied it to the free electromagnetic field as photons.

Reading speed

Watch on YouTube