**4. Discussion of the optical measurements and results**

As the nanocrystal size increases, the energy of the first excited state decreases qualitatively following particle in a box behavior1. The optical absorption results using Perkin Elmer Lambda 950 spectrometer are indicated in Figure 4.

### **a. Energy Shift and Nano- Crystal Size.**

Using the L E. Brus 1,11,12 model we assume the following:

1. The nanocrystal is spherical with a radius R.

84 Macro to Nano Spectroscopy

60 70 80 90 100 110 120 130

**Reaction time (sec)**

Wavelength (nm)

As the nanocrystal size increases, the energy of the first excited state decreases qualitatively following particle in a box behavior1. The optical absorption results using Perkin Elmer

Fig. 3. The change of wavelength with reaction time

Absorbance

**Wavelenght (nm)**

Fig. 4. UV-Vis spectra of Cd-Se colloidal suspension

Lambda 950 spectrometer are indicated in Figure 4.

Using the L E. Brus 1,11,12 model we assume the following:

**a. Energy Shift and Nano- Crystal Size.** 

**4. Discussion of the optical measurements and results** 


The solution to the spherical Schrödinger equation leads to the energy of the exciton electron hole pair as1:

$$E\_{ex} = \frac{h^2}{8R^2} \left(\frac{1}{m\_e} + \frac{1}{m\_h}\right) - \frac{1.8e^2}{4\pi\varepsilon\_{CdSe}\varepsilon\_0 R} + \frac{e^2}{R} \left\langle \sum\_{k=1}^{\infty} \alpha\_k \left(\frac{S}{R}\right)^{2k} \right\rangle$$

The first term is the kinetic energy and the second term the Coulomb potential attractive energy; and the third term is the polarization energy.

#### **b. Using the first term to calculate the exciton energy**

At small R the predominant term is the first term (because of the inverse square R dependence since R<1 for a simple example <sup>2</sup> 1 1 (0.5) 0.5 ).

We can therefore use the first term to approximate R the radius of the nanoparticles as follows:

The energy needed to create the first peak – corresponding to the peak position in the spectra is *u g ex EEE* this energy corresponds to 500 nm from Figure 4.

The energy then converts to 2.48 eV (using the well known conversion formula 1.24 1*m* for

photon energy to eV.

The energy gap of bulk CdSe corresponds to 730 nm (0.73 μm ) and is 1.70 eV [1,10]

This leads to the exciton energy of 0.78 eV

Using the formula:

$$E\_{ex} = \frac{h^2}{8R^2} \left(\frac{1}{m\_e} + \frac{1}{m\_h}\right) - \frac{1.8e^2}{4\pi\varepsilon\_{CdSe}\varepsilon\_0 R} + \frac{e^2}{R} \left\langle \sum\_{k=1}^{\infty} \alpha\_k \left(\frac{S}{R}\right)^{2k} \right\rangle$$

and the first term alone as the approximation for small R

$$E\_{ex} = \frac{h^2}{8R^2} \left(\frac{1}{m\_e} + \frac{1}{m\_h}\right) = 0.78eV$$

Using h as Planck's constant ; the electron effective mass me = 0.13 mass of a free electron and mh equals 0.45 times the free electron mass

R can then be calculated to be the following:

**6** 

*Italy* 

Rita Giovannetti

**The Use of Spectrophotometry UV-Vis** 

*University of Camerino, Chemistry Section of School of Environmental Sciences, Camerino* 

The porphyrins (Fig. 1) are an important class of naturally occurring macrocyclic compounds found in biological compounds that play a very important role in the metabolism of living organisms. They have a universal biological distribution and were involved in the oldest metabolic phenomena on earth. Some of the best examples are the iron-containing porphyrins found as heme (of haemoglobin) and the magnesium-containing reduced porphyrin (or chlorine) found in chlorophyll. Without porphyrins and their relative compounds, life as we know it would be impossible and therefore the knowledge of these systems and their excited states is essential in understanding a wide variety of biological processes, including oxygen binding, electron transfer, catalysis, and the initial

The word porphyrin is derived from the Greek porphura meaning purple. They are in fact a large class of deeply coloured pigment, of natural or synthetic origin, having in common a substituted aromatic macrocycle ring and consists of four pyrrole rings linked by four

The porphyrins have attracted considerable attention because are ubiquitous in natural systems and have prospective applications in mimicking enzymes, catalytic reactions, photodynamic therapy, molecular electronic devices and conversion of solar energy. In particular, numerous porphyrins based artificial light-harvesting antennae, and donor acceptor dyads and triads have been prepared and tested to improve our understanding of

**1. Introduction** 

photochemical step in photosynthesis.

Fig. 1. The structure of porphyrin.

**methine bridge** 

methine bridges (Milgrom, 1997; D. Dolphin, 1978).

the photochemical aspect of natural photosynthesis.

**for the Study of Porphyrins** 

$$R^2 = \frac{h^2}{8E\_{ex}} \left(\frac{1}{m\_e} + \frac{1}{m\_h}\right)$$

$$R = \sqrt{\frac{(6.626)^2 \ge 10^{-68} \ge 9.91452}{9.1095 \ge 10^{-31} \ge 8 \ge 0.78 \ge 1.602 \ge 10^{-19}}} = 2.18 \ge 10^{-9} m \dots$$

This leads to diameter of about 4 nm
