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Photonix

Photoelectric Effect Physics

\[K_{\max} = hf - \phi\]
$21.99 USD
$21.99 USD
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Why can dim ultraviolet light free electrons when bright red light cannot? Photonix knows. Light arrives in quanta of energy hf. Each photon frees one electron with at most Kmax = hf − φ, so frequency sets the energy and brightness only sets the number. Einstein explained it in 1905. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Shipping calculated at checkout by destination.

Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Light delivers energy in photons of hf. An electron can only escape a metal if one photon gives it more than the work function, and the leftover becomes its kinetic energy. Brighter light means more electrons, not faster ones.

Photonix knows that the colour of light matters more than how bright it is.

Shine light on a clean metal and it can knock electrons out. But below a certain frequency nothing comes out, however bright the light. Above it, electrons appear at once, even in dim light. Classical waves could not explain that.

In 1905 Einstein proposed that light arrives in quanta of energy hf. Each quantum gives all its energy to one electron. The electron must spend at least the work function to escape, and keeps the rest as kinetic energy: the equation on this mug. Brighter light means more quanta and more electrons, not faster ones. Robert Millikan tested the straight-line relation carefully and published in 1916. Einstein's 1921 Nobel Prize was given especially for this law.

COLOUR BEATS BRIGHTNESS. Colour here stands for frequency. For many metals the threshold lies in the ultraviolet, beyond any visible colour, which is why dim ultraviolet can free electrons where bright red cannot.

Photonix does not care how many of you shine at her. She cares how hard each one hits.

Equations

\[K_{\max} = hf - \phi\]
SymbolMeaningUnit
\(K_{\max}\) maximum kinetic energy of an ejected electron \(\mathrm{J}\)
\(h\) Planck constant \(\mathrm{J·s}\)
\(f\) frequency of the light \(\mathrm{Hz}\)
\(\phi\) work function: minimum energy to free an electron from the metal \(\mathrm{J}\)

Sources

  1. Einstein (1905) Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt, Ann. Phys. 322, 132
  2. Millikan (1916) A Direct Photoelectric Determination of Planck’s h, Phys. Rev. 7, 355
  3. NobelPrize.org — The Nobel Prize in Physics 1921 (Einstein, "especially for his discovery of the law of the photoelectric effect")
  4. HyperPhysics — Photoelectric Effect
  5. NIST CODATA 2022 — Planck constant h

Source Einstein, A. (1905). Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik 322, 132–148.doi.org/10.1002/andp.19053220607

Field notes

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