We can model the 1,3,5-hexatriene as a box of length 0.904 nm, with 6 electrons in the first three energy levels. What is the frequency of an electronic transition from the highest-occupied orbital to the lowest-unoccupied orbital?

v = 7.85 × 10¹⁴ Hz

Explanation:

The first three energy level can be represented as follows:

⇅ ------> n₄ = 4

⇅ ------> n₃ = 3

⇅ ------> n₂  = 0

ΔE = hv =

ΔE = hv =

ΔE = hv =

ΔE = hv =

where h = planck constant = J.s

mass (m) =

e = 0.904 nm =

hv =

hv =

hv =  

hv = J

v =

v =

v =  

v = 7.85 × 10¹⁴ Hz     (since s⁻¹ is equivalent to 1 Hz)

Thus, the frequency of an electronic transition from the highest-occupied orbital to the lowest-unoccupied orbital = 7.85 × 10¹⁴ Hz