Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: Un(x) = sin () The corresponding energy (level) for each wavefunction solution is: n?h? En 8mL2 a) Is the particle always uniformly distributed throughout the box? Explain your answer. b) Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Follow from Ex 4.7 in the textbook, let's assume that the 1o electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this "molecular box", 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? What's the smallest frequency of light that can excite the electron? Briefly explain why. Note that the length of a C-C bond is about 1.54A and the length of a C=C bond is 1.34A to allow you to estimate the length of the "molecular box".
Consider a particle trapped in a iD box with zero potential energy with walls at x = 0 and x = L. The general wavefunction solutions for this problem with quantum number, n, are: Un(x) = sin () The corresponding energy (level) for each wavefunction solution is: n?h? En 8mL2 a) Is the particle always uniformly distributed throughout the box? Explain your answer. b) Consider the molecules: CH2=CH-CH=CH-CH=CH-CH=CH-CH=CH2. Follow from Ex 4.7 in the textbook, let's assume that the 1o electrons that make up the double bonds can exist everywhere along the carbon chains. The electrons can then be considered as particles in a box; the ends of the molecule correspond to the boundaries of the box with a finite or zero potential energy inside. In this "molecular box", 2 electrons can occupy an energy level. What are quantum states that the electrons from this molecule can occupy in the ground state? What's the smallest frequency of light that can excite the electron? Briefly explain why. Note that the length of a C-C bond is about 1.54A and the length of a C=C bond is 1.34A to allow you to estimate the length of the "molecular box".
Chemistry: The Molecular Science
5th Edition
ISBN:9781285199047
Author:John W. Moore, Conrad L. Stanitski
Publisher:John W. Moore, Conrad L. Stanitski
Chapter5: Electron Configurations And The Periodic Table
Section: Chapter Questions
Problem 5.ACP
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