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 then = 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. n?h? En = Planck's constant = 6.626 x 10-34 J.s; Mass of Electron = 9.109 x 10-28, Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1
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 then = 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. n?h? En = Planck's constant = 6.626 x 10-34 J.s; Mass of Electron = 9.109 x 10-28, Rydberg constant = 1.097 x 107 m-1; Speed of Light = 2.998 x 108 m·s-1
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
Related questions
Question

Transcribed Image Text: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 then = 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.
n²h?
En =
8m.L?
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 fr the required energy to promote an electron
from the n = 2 to n = 5 lever
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
dit
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 2 images

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.Recommended textbooks for you

Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning

Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education

Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning

Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning

Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education

Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning

Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education

Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning

Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY