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- β-Carotene (1) is a linear polyene in which 10 sing le and 11 double bonds alternate along a chain of 22 carbon atoms. If the length of each CC bond is taken to be about 140 pm , then the length L of the molecular box in β-carotene is L = 2.94 nm. Estimate the wavelength of the light absorbed bythis molecule when it undergoes a t rans it ion from its ground state to the next higher excited state.Prove that the potential energy of the electron is Etotal -e?/ (8πεoΥ)5. Sketch the Radial Distribution Function 4xr³R² vs. r for 4s . ● . ● 5s 4p • • 5p • 6s бр 4d,²-²
- 5. Using a table of Hermite Polynomials, provide the property normalized 42. You may 1 (as verify your answer with: n(x) = (21)² H₂ (α²x) e-x² 2nn! 2.Write the valence bond wavefunction for the one cr andtwo n bonds in a nitrogen molecule, N2 .What are differences between n→π* and π →π* bonding electron transition in Fluorescence? Please answer shorty at your own words. Answer should be to the point.
- In the methane molecule, CH4, each hydrogen atom is at the corner of a regular tetrahedron with the carbon atom at the center. If one of the C-H is in the direction of A= î +7 + k and an adjacent C-H bond is at the direction B=î-7-R. results to an angular bond of approximately 109° for a static frozen molecule. However, the molecule we can encounter everyday continuously vibrates and interact with the surrounding causing its bond vector to vary slightly. According to a new spectroscopy analysis, the adjacent bond vectors was found to be A = 1.08i + 0.89j + 1.08k B = 0.85i + -0.93j + -0.94k What is the angle (in degrees) between the bonds based on this new data? Note: Only 1% of error is permitted for the correct answer. IDeter mine the rote low ex pression for the following reetion and give units for K. 3Hz t Al, (so4dzE7B.3(b) Which of the following functions can be normalized (in all cases the range for x is from x = -∞ to ∞, and a is a positive constant): (i) sin(ax); (ii) cos(ax) ex²? Which of these functions are acceptable as wavefunctions?
- a) Determine the LCAO representation for in-phase and out-of-phase orbitals ofH in H20 C2 0,(xz) 0,(yz) b) Determine the two (2) wave functions for the LGO of H2O with the given character tables. Use Nas the Normalization Factor. C2, E A 1 A, 1 C2 o,(rz) o,(yz) C2 2 0,(x2) E 1 1 1. -1 -1 2 B1 В2 1 1 -1 -1 -1 -1determine the normalized wave function for _ = c1(1sA – 18B). In other words find the normalization constant. No S = overlap integral O" = ats (18A - 1sp) 18B) V2(1–S) O b) ab_ = v2(18A – 18B) Od = (194– 19) O d ab_ = /2(1 – S)(1sa – 18B)The Morse potential energy is very useful as a simple representation of the actual molecular potential energy. When 85Rb1H was studied, it was found that ˜ν = 936.8 cm−1 and x_eν˜ = 14.15 cm−1. Plot the potential energy curve from 50 pm to 800 pm aroundRe = 236.7 pm. Then go on to explore how the rotation of a molecule may weaken its bond by allowing for the kinetic energy of rotation of a molecule and plotting V∗ = V + hcBJ˜ (J + 1) with B˜. Plot these curves on the same diagram for J = 40, 80, and 100, and observe how the dissociation energy is affected by the rotations. Hints: Taking B˜ = 3.020 cm−1 as the equilibrium bond length will greatly simplify the calculation. The mass of 85Rb is 84.9118mu