QNT-08

Planck–Einstein relation

E = h f = h c / λ.

Reading speed

PhotonsPlanck 1900

Governing equation

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

where

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

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

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

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