The Pauli exclusion principle limits the number of electrons in any given energy level to two and these two electrons must have opposite spins: +1/2 and -1/2. The quantum mechanical solution for the energy levels of this model is: (1)Īnd m is the mass of an electron and h is Planck's constant. We shall assume that the potentialĮnergy is constant along the chain and that it rises sharply to infinity at the ends i.e., the electron system is replaced by free electrons moving in a onedimensional box of length a. The extra valence electrons on the carbon atoms in the chain and the three remaining electrons on the two nitrogens form a mobile cloud of electrons along the chain (above and below the plane of the chain). Each carbon atom in the chain and each nitrogen at the end is involved in bonding with three atoms by three localized bonds. Thus all the bonds along this chain can be considered equivalent, with bond order 1.5 (similar to the C-C bonds in benzene). The cation can "resonate" between the two limiting structures that is, the wave function for the ion has equal contributions from both states. As an example, consider a dilute solution of 1,1'-diethyl- 4,4'-carbocyanine iodide: We shall present here the simple free-electron model first proposed by Kuhn this model contains some drastic assumptions but has proved reasonably successful for molecules like a conjugated dye. Bond orbital and molecular orbital calculations have been made for these dyes, but the predicted wavelengths are in poor agreement with the observed values. The wavelengths of these bands depends on the spacing of the electronic energy levels. The visible bands for polymethine dyes arise from electronic transitions involving the π electrons along the polymethine chain. In this experiment we are concerned with the determination of the visible absorption spectrum of several symmetrical polymethine dyes and with the interpretation of these spectra using the "free-electron" model. Those compounds which are colored (i.e., absorb in the visible) generally have some weakly bound or delocalized electrons such as the odd electron in a free radical or the electrons in a conjugated organic molecule. In many substances, the lowest excited electronic state is more than 280 kJ above the ground state and no visible spectrum is observed. Particle in a Box : Absorption Spectrum of Conjugated Dyes Part A – Recording the Spectra and Theoretical determination of λmax Theory Absorption bands in the visible region of the spectrum (350 - 700 nm) correspond to transitions from the ground state of a molecule to an excited electronic state which is 160 to 280 kJ above the ground state.
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