Use the particle in a box model to estimate the energies of the first electronicallyexcited states...

Use the particle in a box model to estimate the energies of the first electronicallyexcited states of ethylene, butadiene and hexatriene. Use a table of bond lengths to estimate the length of the box

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Expert Solution

In this experiment, you will carry out absorbance measurements on three conjugated dyes for which particle-in-a-box theory works very well. The compounds are 1,4-diphenyl-1,3-butadiene; 1,6-diphenyl-1,3,5-hexatriene; and 1,8-diphenyl-1,3,5,7-octatetraene. The chemical structures are shown below.

Procedure for The Particle in a Box

Obtain the three pre-filled cuvettes corresponding to each of the following: 1,4-diphenyl-1,3-butadiene; 1,6-diphenyl-1,3,5-hexatriene; and 1,8-diphenyl-1,3,5,7-octatetraene. Each compound has been dissolved in cyclohexane and placed in a capped cuvette and labelled accordingly with "1,4" "1,6" or "1,8." Please do not uncap or discard the solutions in the pre-filled cuvettes.

You will use the OceanOptics spectrophotometer to acquire spectra of these compounds. Be sure to re-calibrate the instrument. Will you continue to use water as your calibration blank, as you did in Part A? After calibration, adjust the x-axis (wavelength) display range to 345 nm-445 nm. This particular spectrometer is not designed for operation below 345 nm, and we are presently not interested in measuring the absorbance above 445 nm.

As you acquire and save each spectrum, be sure to record the lowest-energy (i.e., longest wavelength) local maximum in the absorbance mode, or ?max , to help you interpret the spectral data.

The particle in a one-dimensional box model is a simple quantum mechanical model that can be used to predict the electronic energy levels for the pi electrons in long-chain conjugated unsaturated compounds. This exercise compares the results predicted by the particle-in-a-box model with semi-empirical quantum mechanical calculations.

According to the particle in a 1-D box model, the energy of the electron in a quantum state n is given by:

En = n²h²/8ml²

where h is the Planck's constant, m is the mass of the electron, and l is the length of polyyne. The length of the box is estimated using the C-C triple, single, and C-H bond lengths. The number of pi electrons is 4 times the number of triple bonds in the conjugated polyyne. The HOMO (n) is one half the number of pi electrons. The energy change corresponding to the HOMO-LUMO transition is given by:

DE = E_n+1 - E_n

The wavelength corresponding to the transition is calculated as:

l_max = hc/DE

queen_honey_blossom answered 7 months ago

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