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

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