the orange dot

LITIn a semiconductor nanocrystal the electron and hole are squeezed, so a smaller dot emits bluer light. The Brus model gives E(r) = E_gap + (h²/8r²)(1/m_e* + 1/m_h*) − 1.786 e²/(4πε₀ε r). For CdSe: E_gap = 1.74 eV, m_e* = 0.13, m_h* = 0.45, ε ≈ 9.6–10.6 (values vary by source). Brus (1984, 1986); the 2023 Nobel Prize in Chemistry was for quantum dots.

COMPUTEDSolving Brus (with the Coulomb term, ε = 9.6) for 600 nm orange gives a diameter of about 6.0 nm, consistent with the 5–6 nm usually quoted. A 4 nm dot comes out blue-green in this model. The effective-mass model is known to be rough for small dots, and empirical sizing curves can differ; treat the size as a model estimate. A row of vials glows under UV; the −/+ pair is a dot one step smaller (yellower) and one step larger (redder) than the orange one.

diameter solve for 600 nm

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