Question

A simple cyanine dye molecule has a long central carbon chain, with a total of 8 bonds, between the two nitrogen atoms. One electron per bond is essentially free to move up and down this chain. The potential energy for such an electron can be modeled as a one-dimensional box. The distance between each bond is about 0.14 nm.
What would be the transition corresponding to the lowest energy photon that this molecule could absorb? Would such a photon be in the visible range?

Answer 1

Answer:

For one dimensional box

E= $n^{2}h^{2}/ 8mL^{2}$

For lowest energy transition will be from n =1 to n=2

Hence,

$hc/\lambda = 2^{2}h^{2}/ 8mL^{2} - h^{2}/8mL^{2}$

h= 6.626 *10-34 J.s

m = 9.31 *10-31 Kg

L= 0.14 * 10-9 m

c= 3 *108 m/s

$\lambda = 8*c*m*L^{2} / 3*h$

$\lambda = 22 nm$

Not in visible range