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QNT-14

Photoelectric equation

Kmax = hf − φ. Light above the work function frees electrons.

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QuantaEinstein 1905

Governing equation

Kmax⁡=hf−φK_{\max}=hf-\varphi

f∈[0.2,2]f \in \left[0.2, 2\right]

where

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

The figure, part by part

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QNT-14 · quantum
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①

Governing law — red

Kmax⁡=hf−φK_{\max}=hf-\varphi

f∈[0.2,2]f \in \left[0.2, 2\right]

f=0.2f = 0.2Kmax=−1.473K_{max} = -1.473

②

Domain of the variable — blue

fmin⁡=0.2,fmax⁡=2f_{\min} = 0.2,\quad f_{\max} = 2

f∈[0.2,2]f \in \left[0.2, 2\right]

f=0.2f = 0.2f=0.2f = 0.2

③

Response curve — green

Kmax⁡=hf−φK_{\max}=hf-\varphi

f∈[0.2,2]f \in \left[0.2, 2\right]

f=0.2f = 0.2Kmax=−1.473K_{max} = -1.473

④

Rate of change — amber

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

f∈[0.2,2]f \in \left[0.2, 2\right]

f=0.211f = 0.211Kmax′=4.136K_{max}^{\prime} = 4.136

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-14 — Photoelectric equation) is the form associated with Einstein 1905. Working symbols: ff, φ\varphi →\rightarrow KmaxK_{max}. Stopping potential e Vs = Kmax. Intensity sets the current, not Kmax.

Purpose

Purpose: compute KmaxK_{max} from ff, φ\varphi in Quantum mechanics via Kmax⁡=hf−φK_{\max}=hf-\varphi Kmax = hf − φ. Light above the work function frees electrons. 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=0.800 PHzf = 0.800\,\mathrm{PHz}, φ=2.300 eV\varphi = 2.300\,\mathrm{eV}, the governing relation Kmax⁡=hf−φK_{\max}=hf-\varphi yields Kmax=1.009 eVK_{max} = 1.009\,\mathrm{eV}. A metal, a photon, an escaping electron. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Outputs

  • Max kinetic energy K_{max}1.009 eV
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QNT-14 · quantum
00:0 / 00:08

Narration of this film

A metal, a photon, an escaping electron.

Stopping potential e Vs = Kmax. Intensity sets the current, not Kmax.

Reading speed

Watch on YouTube