Skip to main content
Ch. 8 - Delocalized Electrons: Their Effect on Stability, pKa, and the Products of a Reaction • Aromaticity and Electronic Effects: An Introduction to the Reactions of Benzene
Bruice - Organic Chemistry 8th Edition
Bruice8th EditionOrganic ChemistryISBN: 9780135213711당신이 사용하는 게 아니라요?교과서 변경
8장, 문제 86g

Answer the following questions for the molecular orbitals (MOs) of 1,3,5,7-octatetraene:
g. How many nodes does the highest-energy MO of 1,3,5,7-octatetraene have between the nuclei?

검증된 단계별 안내
1
Identify the number of π-electrons in 1,3,5,7-octatetraene. Each double bond contributes 2 π-electrons, and there are 4 double bonds, so the molecule has 8 π-electrons.
Determine the number of molecular orbitals (MOs) formed. For 8 π-electrons, there will be 8 π-MOs, labeled as Ψ₁, Ψ₂, Ψ₃, ..., Ψ₈, with Ψ₁ being the lowest-energy MO and Ψ₈ being the highest-energy MO.
Recall that the number of nodes in a molecular orbital increases as the energy of the MO increases. The number of nodes in a given MO is equal to (n - 1), where n is the MO's index (e.g., Ψ₁ has 0 nodes, Ψ₂ has 1 node, etc.).
For the highest-energy MO (Ψ₈), calculate the number of nodes using the formula (n - 1). Since n = 8 for Ψ₈, the number of nodes is (8 - 1) = 7.
Conclude that the highest-energy MO of 1,3,5,7-octatetraene has 7 nodes between the nuclei.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Molecular Orbitals (MOs)

Molecular orbitals are formed by the linear combination of atomic orbitals (LCAO) and describe the behavior of electrons in a molecule. They can be bonding, antibonding, or non-bonding, depending on the phase relationship of the combining atomic orbitals. The energy levels of MOs are crucial for understanding the electronic structure and reactivity of molecules.
추천 영상:
08:41
Review of Molecular Orbitals

Nodes in Molecular Orbitals

Nodes are regions in a molecular orbital where the probability of finding an electron is zero. The number of nodes in a MO is related to its energy level; higher energy MOs have more nodes. For a given molecular system, the number of nodes can be determined using the formula: number of nodes = n - 1, where n is the principal quantum number of the MO.
추천 영상:
08:41
Review of Molecular Orbitals

Octatetraene Structure

1,3,5,7-octatetraene is a linear conjugated hydrocarbon with alternating double bonds. Its structure allows for delocalization of π electrons across the molecule, which influences the energy levels of its molecular orbitals. Understanding the arrangement of these double bonds is essential for predicting the number of nodes in the highest-energy MO, as it directly affects the electron distribution and energy states.
추천 영상:
03:04
Drawing Resonance Structures