Podcast Beta
Questions and Answers
What is the total bond length of the double bonds in CH2=CH-CH=CH-CH=CH2?
The total bond length of the double bonds is 402 pm.
Calculate the bond length for the single bonds in CH2=CH-CH=CH-CH=CH2.
The total bond length for the single bonds is 308 pm.
What is the calculated value of 'a' for the molecular structure given?
The value of 'a' is 864 pm.
How do the energy levels E2 and E1 in the equation E= n² h² / 8ma² compare?
Signup and view all the answers
What is the relation of E7 to E4 in the energy level of the molecular structure?
Signup and view all the answers
What is the formula for calculating the energy of the HOMO level in a 2ne system?
Signup and view all the answers
How can you derive the expression for the energy difference ΔE between the HOMO and LUMO?
Signup and view all the answers
What is the relationship between ΔELUMO - HOMO and the quantum number n?
Signup and view all the answers
If a compound has a ΔE LOMO - HOMO of 9.02 x 10⁻¹⁹ J, how can you express this in terms of frequency or wavenumber?
Signup and view all the answers
What does Ψ₁(2) represent in the context of molecular vibrations for CH₂=CH-CH-CH₂?
Signup and view all the answers
Study Notes
Molecular Structure and Bond Lengths
- Hexatriene structure: CH2=CH-CH=CH-CH=CH2.
- Bond lengths:
- C=C bonds measure 134 pm (3 bonds, total = 402 pm).
- C-C bonds measure 154 pm (2 bonds, total = 308 pm).
- Average bond length calculated as 154 pm.
- Effective length 'a' for hexatriene is 864 pm.
Electronic Energy Levels
- Energy formula: E = n²h² / 8ma², where 'n' is the quantum number, 'h' is Planck's constant, 'm' is mass, and 'a' is the box length.
- Ground state (n=1): ψ1(2) = (h² / 8m * 864²) x 2.
- Energy levels for n=2 to n=7 are computed similarly using the formula.
HOMO and LUMO
- Two-electron system distinguishes between HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital).
- HOMO energy level: En = n²h² / 8ma².
- LUMO energy level (n+1) has a corresponding energy calculation: En+1 = (n+1)²h² / 8ma².
- The energy difference ΔE between LUMO and HOMO is determined as ΔE = (2n+1)h² / 8ma².
Energy Calculations
- For CH2=CH-CH=CH2, 'a' is 578 pm; ΔE between LUMO and HOMO is 9.02 x 10⁻¹⁹ J.
- Frequency and wavenumber calculated as ΔE/hc ≈ 4.61 x 10⁴.
Molecular Vibrational States
- ψ₁(2) and ψ₂(2) derived from vibrational analysis of CH₂=CH-CH-CH₂.
- Integrals solve for wave functions within defined conditions.
Boundary Conditions for Wave Function
- Two primary conditions for wave function Ψ:
- At x = 0, Ψ = 0 implies B = 0.
- At Ψ = 0 and x = a, this leads to sine conditions where 0 = sin(k).
Energy Drift and Differences
- Defined energy levels for n states:
- E1 (n=1), E2 (n=2), and E3 (n=3) follow the formula E = n²h² / 8ma².
- Energy difference ΔE between consecutive levels computed as ΔE = E2 - E1 and ΔE = E3 - E2.
Particle in a Box Model
- Characterization of quantum states where potential energy outside the box is infinite while inside it is zero.
- Wave functions defined within the box using Ψ = √(2/a)sin(nπ/a x).
3D Schrödinger Equation
- General form of the 3D equation incorporates second derivatives along each axis and considers potential energy (V).
Atomic Orbitals and Energy Transition
- Atomic orbital defined in terms of 3D space surrounding the nucleus.
- Energy required to promote electrons from HOMO to LUMO calculated for linear hexatriene systems.
Summary of Energy Levels
- Energy levels and wave function characteristics calculated for n from 0 upwards; concludes with HOMO at n = 1/2 and LUMO at n = 3/2.
- The wave function Ψ is normalized to the total probability of finding an electron within the defined region.
Electron Configuration in Conjugated Systems
- Conjugate molecules possess overlapping p-orbitals across three or more atoms, affecting their electronic properties.
- Provided calculations focus on the structural geometries inherent in conjugated molecules emphasizing atomic characteristics.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Related Documents
Description
Explore the concepts of electronic systems, focusing on HOMO and LUMO energies, as well as the calculation of molecular vibrations. This quiz covers important formulas and calculations relevant to quantum chemistry. Dive into topics like ΔE calculations and frequency determination for organic compounds.
