1a.

1b. The largest peak would have been created by the energy transition of an electron from HOMO to LUMO whereas the smaller peak would have been created by the energy transition of an electron from a lower energy level that is not the HOMO to an excited state.

Another explanation for the creation of the smaller peak would be the interaction of the magnetic field generated from the spectrophotometer and the electrons of the atoms. However, since this does not frequently occur it would not generate a large peak.

1c. When UV light hits the plastic, the degradation of the plastic under the UV light would result in a faulty transmission and inaccurate spectrum of absorbance.

In order to see this region, we could use a material like quartz which will allow a more clear transmission of UV light and will not degrade when radiated by it.

1d. It will be cut approximately in half since there is approximately one-half less dye to absorb the incoming radiation.

2a.

**Figure1. Graph of Absorbance vs Wavelength for 2,2' Dyes**

**Figure2. Graph of Absorbance vs Wavelength for 4,4' Dyes**

2b.

Wavelength (nm) | Absorbance | Wavlength (nm) | Absorbance | ||

2,2' C23H23N2I | 472.997406 | 0.84564775 | 4,4' C23H23N2I | 538.982056 | 0.40029025 |

2,2' C25H25N2I | 554.009949 | 0.88385493 | 4,4' C25H25N2I | 656.494385 | 1.25485635 |

2,2' C27H27N2I | 657.513367 | 0.67185462 | 4,4' C27H27N2I | 767.985352 | 0.42982915 |

2c. The predictions from the pre-lab and the measured wavelengths differ quite significantly, mostly by a couple hundred nanometers. One possible explanation for this is that we assumed that the nitrogen atoms were the infinite potential energy ends of the boxes in our pre-lab, but that is not what happens in reality. Therefore, the values we get from making this assumptions in our pre-lab would be very different from the measured values based on a more realistic model.

2d.

Concentration (M) | Absorption | Number of Bonds | Molar Absorptivity (M=1 cm-1) | |

2,2' C23H23N2I | 5.06E-06 | 0.84564775 | 4 | 4.18E+04 |

2,2' C25H25N2I | 4.99E-06 | 0.88385493 | 6 | 2.95E+04 |

2,2' C27H27N2I | 4.99E-06 | 0.67185462 | 8 | 1.68E+04 |

4,4' C23H23N2I | 1.01E-05 | 0.40029025 | 8 | 4.95E+03 |

4,4' C25H25N2I | 4.99E-06 | 1.25485635 | 10 | 2.51E+04 |

4,4' C27H27N2I | 4.99E-06 | 0.42982915 | 12 | 7.18E+03 |

3a.

b | N | Numerator | Denominator | Wavlength (m) | Wavelength (nm) |

6 | 6 | 1.54164E-39 | 4.6382E-33 | 3.3238E-07 | 332.379788 |

10 | 10 | 4.28234E-39 | 7.2886E-33 | 5.8754E-07 | 587.54003 |

8 | 8 | 2.7407E-39 | 5.9634E-33 | 4.59587E-07 | 459.586868 |

12 | 12 | 6.16658E-39 | 8.6138E-33 | 7.15895E-07 | 715.894928 |

10 | 10 | 4.28234E-39 | 7.2886E-33 | 5.8754E-07 | 587.54003 |

14 | 14 | 8.39339E-39 | 9.939E-33 | 8.44491E-07 | 844.490869 |

3b. B predicts the wavelengths better than A since in A we assumed that the electrons were trapped in two walls of infinite potential energy, however since the electrons are delocalized onto these atoms, this isn't a realistic to expect. Since model B describes a more realistic model of the atoms and the pathway of the electrons, the predicted wavelengths will also be closer to the measured wavelengths as well.

4a.

4b.

Wavelength (m) | N | Numerator | Denominator | L (m) | |

2,2' C23H23N2I | 4.72997E-07 | 6 | 2.1939E-39 | 2.1849E-21 | 1.0021E-09 |

2,2' C25H25N2I | 5.5401E-07 | 8 | 3.3038E-39 | 2.1849E-21 | 1.2297E-09 |

2,2' C27H27N2I | 6.57513E-07 | 10 | 4.7924E-39 | 2.1849E-21 | 1.481E-09 |

4,4' C23H23N2I | 5.38982E-07 | 10 | 3.9284E-39 | 2.1849E-21 | 1.3409E-09 |

4,4' C25H25N2I | 6.56494E-07 | 12 | 5.6549E-39 | 2.1849E-21 | 1.6088E-09 |

4,4' C27H27N2I | 7.67985E-07 | 14 | 7.633E-39 | 2.1849E-21 | 1.8691E-09 |

5a.

**Figure3. Length of Box vs Number of Bonds for 2,2' Dyes**

**Figure4. Length of Box vs Number of Bonds for 4,4' Dyes**

5b. In reality, atoms are modeled in three dimensions. For this lab, we used values obtained from three-dimensional models in equations based on the one-dimensional particle in a box in order to calculate the bond length. Therefore, the values we obtained form our calculations are not completely accurate because the constants and equations are based on two different dimensions.

6a. Model A is insufficient because it assumed that the ends of the boxes were the nitrogen atoms of infinite potential energy when in fact this is not true. The realistic model is more complicated and the electrons can travel beyond these nitrogen atom boundaries, which is why Model B becomes more accurate by including two extra bonds that the electrons can occupy beyond the nitrogen atom boundaries.

6b. One assumption that we made was that the potential energy between the nitrogen atoms was equal to zero which was based off our assumptions of an electron trapped in a one dimensional box. In reality however, electrons will interact with other electrons and nuclei of other atoms to create a potential energy that is greater than zero.

Another assumption we made was that all the bonds are like the C-C bonds in benzene when in reality there are many different types of bonds that construct the molecules. Bonds created from C-N interactions as well as bonds of a higher order between C-C atoms would yield different lengths. We used a general measurement and applied it to the formulas to obtain a value that would be a bit off.

Finally, we used the bond length of benzene, which is a three dimensional molecule, to solve for the equations of a one-dimensional molecule. The differences in dimensions would account for differences in values based on the equations.

6c. One modification that we that we could make is modify the one dimensional equations we used to solve for the particle in a box model into more appropriate three dimensional equations to solve for electrons in three-dimensional atoms. Since the constants and measurements we used were based on three-dimensional atoms, changing the equation to a three-dimensional one would make it more compatible and accurate. However, in doing so, solving the three dimensional Schrodinger equation would require a distance from the nucleus (r), a longitudinal value (ÃÂ¤**),** and a latitude value (ÃÂ) which would make the equation more complex. These three numbers represent the three quantum numbers n, l, ml respectively and can ultimately allow for more realistic and accurate answers. Furthermore, if we were to adopt a 3-d model, we would now have to consider the potential energy in order to solve the Schrodinger equation as now that is represented by the angular dependence. Also, the lengths of the boxes of all three dimensions would have to be measured.

6d. We can create a graph of Absorbance vs Concentration of the dye and plot points of varying concentrations and then create a trendline from these points. Since absorbance is directly proportional to concentration, the trendline should also have a positive slope. Using this trendline, you are able to find a corresponding concentration value for every absorbance value for this dye and therefore be able to extrapolate different concentrations by only knowing the absorbance of the dye.