Absorption intensities of electronic transitions (25%) Consider a conjugated cha
ID: 945374 • Letter: A
Question
Absorption intensities of electronic transitions (25%) Consider a conjugated chain of 2n C-atoms. We treat the pi orbitals with the one-dimensional particle in a box model. The box length is L = (2n + 1)R where R is the average linear C-C distance. For 2n carbon atoms, a polyene chain has n doubly occupied pi orbitals. Calculate the oscillator strength (light polarization in x direction) for the 'HOMO-LUMO transition' (n right arrow n + 1) as a function of R. Delta E = pie^2/2R. 1/L; integrate^pi_0 y. sin[ny]. sin[(n + 1)y]dy = -1 + 1/(2n + 1)^2 approximately equal to -1 (you may use the approximation for the integral) How does the molar absorption coefficient vary with the chain length? How does the specific absorption coefficient (per gram) vary with the chain length? Use for the molar mass: 13(2n + 1)Explanation / Answer
In the particle in a box model, the frequency of the lowest energy electronic transition is given by:
= h(N+ 1)/(8ma2)
where N is the number of electrons, and a is the 'length' of the molecular box.
Thus, = h(N+ 1)/(8m(2n+1)2R2)
The magnitude of the oscillator strength ( f ) for an electronic transition is proportional to the square of the transition dipole moment produced by the action of electromagnetic radiation on an electric dipole.
f µ µge2 = (er)2