QNT-03

Einstein photoelectric equation

Kmax = h f − φ.

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PhotonsEinstein 1905

Governing equation

K_{\max}=hf-\varphi,\quad f_c=\varphi/h

$f \in \left[0.1, 5\right]$

where

f: Frequency (PHz)
\varphi: Work function (eV)
K_{\max}: Max kinetic energy (eV)
f_c: Cutoff frequency (PHz)

The figure, part by part

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①

Governing law — red

K_{\max}=hf-\varphi,\quad f_c=\varphi/h

$f \in \left[0.1, 5\right]$

$f = 0.1$ $K_{\max} = -1.886$

Along the curve

②

Domain of the variable — blue

f_{\min} = 0.1,\quad f_{\max} = 5

$f \in \left[0.1, 5\right]$

$f = 0.1$ $f = 0.1$

Along the curve

③

Response curve — green

K_{\max}=hf-\varphi,\quad f_c=\varphi/h

$f \in \left[0.1, 5\right]$

$f = 0.1$ $K_{\max} = -1.886$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}K_{\max}}{\mathrm{d}f}

$f \in \left[0.1, 5\right]$

$f = 0.131$ $K_{\max}^{\prime} = 4.136$

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-03 — Einstein photoelectric equation) is the form associated with Einstein 1905. Working symbols: $f$ , $\varphi$ $\rightarrow$ $K_{\max}$ , $f_c$ . Einstein treated light as quanta of energy hf. Electrons leave a metal with leftover kinetic energy hf − φ, explaining the cutoff frequency.

Purpose

Purpose: compute

K_{\max}

f_c

from

f

\varphi

in Quantum mechanics via

K_{\max}=hf-\varphi,\quad f_c=\varphi/h

Kmax = h f − φ. 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 = 1.000\,\mathrm{PHz}

\varphi = 2.300\,\mathrm{eV}

, the governing relation

K_{\max}=hf-\varphi,\quad f_c=\varphi/h

yields

K_{\max} = 1.8357\,\mathrm{eV}

f_c = 0.5561\,\mathrm{PHz}

. Single photon, one electron, φ in eV, f in PHz (10¹⁵ Hz). Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Frequency f1 PHzWork function \varphi2.3 eV

Outputs

Max kinetic energy K_{\max}1.8357 eV
Cutoff frequency f_c0.5561 PHz

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Narration of this film

Single photon, one electron, φ in eV, f in PHz (10¹⁵ Hz).

Einstein treated light as quanta of energy hf. Electrons leave a metal with leftover kinetic energy hf − φ, explaining the cutoff frequency.

Reading speed

Watch on YouTube