AgCl Photolysis: Latent Image Formation (2D)

Illumination

Wavelength λ 380 nm

E = 3.26 eV (above E_g)

Photon flux 0.30 /s/grain

Sensitivity specks / grain 4

Latent Image Array

Photons absorbed

Ag⁰ atoms formed

Developable grains

0 / 0

Developable fraction

0.0%

Developable fraction vs. exposuret = 0.0 s

How it works

Each square in the array is an independent AgCl photographic grain, the same Gurney-Mott mechanism as classical film, run here across a whole population at once so you can watch the statistics of latent-image formation, not just one crystal.

Photon energy:  E = hc / λ = 1239.84 eV·nm / λ
Absorption:     requires E > E_g ≈ 3.25 eV (band edge of AgCl)
Per photon:     one random grain absorbs it, at one randomly
                chosen sensitivity speck within that grain
Reduction:      Ag⁺(interstitial) + e⁻ → Ag⁰ at that speck
Stability:      a grain is "developable" the moment ANY single
                speck reaches ≥ 4 accumulated Ag⁰ atoms
                (Gurney-Mott, 1938)

This is a genuine stochastic process: photon arrivals are a Poisson process at a rate set by the flux slider, and every absorbed photon lands on a uniformly random speck inside its grain — not always the same one. A grain only becomes developable if enough of its photons happen to land on the same speck before threshold; photons scattered thinly across several specks leave every speck below threshold and the grain never develops, even after absorbing several photons. That is why the developable fraction rises faster than linearly with exposure: at low exposure almost no speck accumulates four hits by chance, but past a knee the odds of at least one speck clustering four hits climb quickly, then saturate as nearly every grain has developed.

Wavelength sets the photon energy. Below the ≈388 nm band edge, photons lack enough energy to cross the gap and are not absorbed at all — a hard threshold, exactly like the photoelectric effect.
Photon flux is the exposure rate per grain — higher flux means more absorbed photons per unit time, so the same clustering statistics play out faster.
Sensitivity specks / grain spreads the same photon budget over more candidate sites: more specks make it statistically harder for any one of them to reach threshold first, so developability drops for a fixed exposure — the real reason coarser-grained, more heavily doped emulsions need more light.
Watch the graph: it plots the developable fraction against elapsed exposure time and is never a straight line — a direct visualization of clustering statistics, not simple linear photon counting.

AgCl grain (undeveloped) photon absorption event speck, Ag⁰ < threshold developable grain (speck ≥ 4 Ag⁰)