Question

Calculate the wavelength required to excite one electron from the HOMO (Highest occupied energy level) to the LUMO (Lowest occupied energy level) for ethylene, and 1,3,5-hexatriene. Consider all systems as all-trans polyenes. Give your answer in nm. Describe the process.

Answer 1

The HOMO-LUMO energy difference in ehtylene is 167 kJ/mol and we need wavelength. Let's see:

The energy of a photon is given by:

Where h is the Planck constant (6.63⋅10⁻³⁴ J⋅s) and v is the frequency.

Frequency is related to wavelength as:

Where c is the speed of light and lambda is the wavelength

Joining these two equations:

The number of photons per mole is given by the Avogadoro number (6.02x10²³):

All we have to do is re-arrange this equation and take into account the fact that the energy pero mole value has to be in Joules:

The transition requires light with a wavelength of 171 nm.

The HOMO-LUMO energy for 1,3,5-hexatriene is 109 kcal/mol, so we have:

,

which turns the requires wavelength to 262 nm.