Quantum dot emission energy is set by size relative to the Bohr radius
Supplied working report; original verdicts not validated.
Review status: Held for correction. This is an archival source note, not a passed proof.
README.md
# Quantum dot emission energy is set by size relative to the Bohr radius **XXII, Theory 13 / Nanoscale / Quantum dots** · verdict: **supported** Claim (verbatim): > Quantum dot emission energy is set by the ratio of dot diameter to exciton Bohr radius, so small changes in size produce large colour shifts only below that scale. ## Result The Brus gap climbs steeply below the Bohr diameter (10.1 nm); the mean magnitude of dE/d(diameter) is 0.66 eV/nm below it and 0.01 eV/nm above it. ## Headline Colour shifts with size are ~102x steeper below the Bohr diameter than above it. ## Design The confined bandgap was computed from the Brus equation for CdSe across 0.8-12 nm diameters, and dE/d(diameter) compared below vs above the exciton Bohr diameter. ## Key statistics - bohr_diameter_nm = 10.0734 nm - mean_abs_dEdD_below_eV_per_nm = 0.658499 eV/nm - mean_abs_dEdD_above_eV_per_nm = 0.00648005 eV/nm ## Predictions - **P1** (supported): 0.66 vs 0.01 eV/nm below vs above the Bohr diameter ## Limitations - The Brus equation is an effective-mass approximation and omits surface states and coupling. - CdSe is one material; the numerical threshold is material-specific even though the qualitative claim is general. - This is a model of the quantum-confinement effect, not a spectrum of a synthesised sample. Provenance: Brus (1984) effective-mass confinement model with standard CdSe parameters. *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*