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This study explores the behavior of delocalized π electrons in conjugated dye molecules through the particle-in-a-box model. It illustrates how these electrons transition between quantized energy states when light is absorbed, leading to measurable absorption spectra. The research analyzes the absorption characteristics of three dye molecules with varying lengths, applying Beer’s Law to correlate absorption intensity with dye concentration. Predictions derived from quantum mechanics are compared to experimental data, enabling the calculation of the molar absorption coefficient and extinction coefficient for one specific dye.
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DIPHENYLPOLYENE DYE SPECTRA UV-VISIBLE SPECTROSCOPY PARTICLE IN THE BOX
QUANTUM MECHANICAL MODEL • Delocalized pi electrons in a conjugated dye molecule are constrained to move along the C-C backbone. • What energy states are the pi electrons in? The particle in the box model provides the answer. • En = n2h2/8mL2 where L is the length of the dye molecule, m is the electron mass, h is Planck’s constant and n is 1,2 ,3…
QM Model - 2 • Light absorbed by the dye molecule will cause the electron to be promoted from ni to nf. • The energy of this transition is ΔE = (nf2 -ni2)h2/8mL2 = hc/ • Measure the absorption spectra for three dye molecules (with increasing L values)
BEER’S LAW • Beer’s Law describes the dependence of absorption intensity on dye molecule concentration, [J]. • A = ε [J]ℓ where ε is the molar absorption coefficient and ℓ is the cell path length. • A linear least analysis of A vs [J] yields ε.
Analysis • Calculate the Particle in the Box predictions for absorption wavelength and compare them to the experimental values. • Modify the Box model using a factor α. • Use the absorbance vs dye concentration data to determine the extinction coefficient for one dye.
