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Vol. 74 No. 8 August 1997 Journal of Chemical Education 985

In the Laboratory

A common experiment in many undergraduate physi-cal chemistry laboratories is the study of how the absorp-tion spectra of polymeth ine dyes can be used t o determinethe box length in the one-dimensional particle-in-a-boxmodel (1, 2). A new series of compounds is proposed to re-place the polymethine dyes in this experiment t ha t a re lessexpensive and less hazardous, and the length of the box iseasier for students to visualize. The compounds are 1,4-dipheny l-1,3-but a diene; 1,6-dipheny l-1,3,5-hexa tr iene; a nd1,8-diphenyl-1,3,5,7-octatetraene.

Experimental Box Length

To begin, ea ch compound is dissolved in cyclohexan e tomake a 106 M solution. Then the absorption spectrum of

each solution is acquired from 300 to 425 nm as shown inFigure 1. For each spectrum, the wavelength of the lowestenergy peak is determined and converted to energy. Thisenergy is used in th e eigenva lue expression shown below forthe one-dimensional particle in a box.

E =

nf

2 n

i

2h

2

8mL 2

To ca lculat e the lengt h, L , of the quantum mechanical (ex-perimental) box, m is taken to be the mass of an electron,and nis the initia l or fina l qua ntu m level for the electronictra nsition. For each compound nis determined by count ingthe number of electrons between the phenyl rings and

then filling the energy levels with pairs of electrons. Thelowest energy transition occurs from the highest occupiedenergy level to the lowest unoccupied energy level (1, 2).For example, 1,4-diphenyl-1,3-butadiene contains 4 elec-trons betw een the phenyl rings. Thus, the tw o lowest q ua n-tum levels are f i l led and the lowest energy transit ion isfrom ni= 2 to nf= 3.

Theoretical Box Length

In this s eries of diphenyl compounds, t he length of thebox is taken to be the distance between the phenyl ringsand the phenyl rings represent the walls of the box. In thepolymethine dy es, the box length includes not only th e dis-tance between the rings, but extends into and beyond the

rings (1, 2). As a result, students have great difficulty pic-tur ing where the wa lls of the box are and wha t length th eyare trying to measure. Students have a better understand-ing of the model when t he diphenyl compounds a re used.

To calcula te th e theoretica l box lengt h for the diphenylcompounds, use 0.139 nm as the average bond length of acarboncarbon bond in the conjugated system between therings. The theoretical box lengths are calculated by deter-mining the number of bonds between the phenyl rings andmultiplying by the length per bond. The theoretical boxlengths a re given in Table 1 along wit h t he experimenta l

Figure 1. Absorption spectra of the diphenyl compounds in cyclo-

hexane: --- 1,4-diphenyl-1,3-butadiene; ... 1,6-diphenyl-1,3,5-

hexatriene; 1,8-diphenyl-1,3,5,7-octatetraene.

Alternative Compounds for the Particle in a Box Experiment

Bruce D. Anderson

Department of Chemistry, Muhlenberg College, Allentown, PA 18104

box lengths determined from the absorption spectra. Thet h e o r e t i c a l a n d e x p e r i m e n t a l b o x l e n g t h s f o r t h epolymethine dyes are included in Table 1 for comparison.

In conclusion, the experimenta l box lengths a re in sur-prisingly good agreement with the theoretical box lengths.Further, the results are comparable to those obtained us-ing the polymethine dyes, but the qua ntu m mechanical boxis much easier for stud ents t o recognize using the diphenylcompounds.

Literature Cited

1. S im e, R. J . Physical Chemistr y: M ethods, Techniqu es, and E xperi -

ments; Saunders College: Philadelphia, 1990; p 687.

2. Shoemaker, D. P. ; Garla nd, C. W.; Nibler, J . W. Experim ents in

Physical Chemistr y; McGr aw -Hill: New York, 1989; p 440.

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