Electrons in molecules can be found in orbitals that extend over more than one atom. Consider  one electron that is confined in a molecular orbital that extends over 8 adjacent carbon atoms.  The electron can move freely between the 8 atoms.    a)  Using  the  one-dimensional  particle-in-the-box  model,  calculate  the  energy  required  to  promote an electron from the n = 2 to the n = 5 level. The length of the box is determined by  the C-C bond distance, which is 139 pm. Note: The following information may or may not be useful.  ?? =  ?2ℎ2 8???2  Planck's constant = 6.626 x 10-34 J·s; Mass of Electron = 9.109 x 10-28 g;   Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1  b)  What frequency of light would cause this excitation? c) Now imagine a straight chain of 2000 carbon atoms. Assume that the orbital extends over  the entire  chain  and  repeat  the  calculation  for  the  required  energy  to promote  an  electron  from the n = 2 to n = 5 level.

2. Electrons in molecules can be found in orbitals that extend over more than one atom. Consider 
one electron that is confined in a molecular orbital that extends over 8 adjacent carbon atoms. 
The electron can move freely between the 8 atoms. 
 
a)  Using  the  one-dimensional  particle-in-the-box  model,  calculate  the  energy  required  to 
promote an electron from the n = 2 to the n = 5 level. The length of the box is determined by 
the C-C bond distance, which is 139 pm.
Note: The following information may or may not be useful. 
?? =  ?2ℎ2
8???2 
Planck's constant = 6.626 x 10-34 J·s; Mass of Electron = 9.109 x 10-28 g;  
Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1 
b)  What frequency of light would cause this excitation?
c) Now imagine a straight chain of 2000 carbon atoms. Assume that the orbital extends over 
the entire  chain  and  repeat  the  calculation  for  the  required  energy  to promote  an  electron 
from the n = 2 to n = 5 level. 
d)  Would you expect the energy levels to get closer or farther apart if you increased the chain 
to one million carbon atoms (i.e approaching bulk properties)? Provide a brief explanation