The particle on a ring can be used as a model for the motion of electrons around the [18]-annulene ring.See a 2-D representation of the [18]-annulene molecule below; the dashed line around the periphery of themolecule indicates the electron path.HHHHHHHHHHHHHHHWe may treat the structure as a circular ring of radius 840 pm, with 18 electrons in the conjugated systemmoving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state isoccupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highestoccupied level, and (b) calculate the frequency of radiation that can induce a transition between the highestoccupied and lowest unoccupied levels.

The [18]-annulene ring has been given to follow the particle in a ring model. The circular radius of…

The particle on a ring can be used as a model for the motion of electrons around the [18]-annulene ring. See a 2-D representation of the [18]-annulene molecule below; the dashed line around the periphery of the molecule indicates the electron path. H H H H H H H H H H H H H We may treat the structure as a circular ring radius 840 pm, with 18 ele trons in conjugated system moving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state is occupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highest occupied level, and (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

The particle on a ring can be used as a model for the motion of electrons around the [18]-annulene ring. See a 2-D representation of the [18]-annulene molecule below; the dashed line around the periphery of the molecule indicates the electron path. H H H H H H H H H H H H H We may treat the structure as a circular ring radius 840 pm, with 18 ele trons in conjugated system moving along the perimeter of the ring. Assuming that, in the ground state of the molecule, each state is occupied by two electrons, (a) calculate the energy and angular momentum of an electron in the highest occupied level, and (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.

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...

See similar textbooks

Similar questions

P18.5 ¹H¹F has a force constant of 966 N m¹ and a bond length of 91.68 pm. Calculate the frequency of the
Using a simple particle-in-a-box model for the multiple bonding in 1,2-butadiene and the n = 2 wave function for the weakest bound electron, calculate the probability of finding the electron in an 0.1 interval centered midway between the two inner carbon atoms (that is, the center is at x = 2.11 Å, so this interval is from x1 = 2.06 Å to x2 = 2.16 Å). Then calculate the probability of finding the electron in an 0.1 interval centered midway between an end carbon atom and the carbon atom that is double-bonded to it in the Lewis dot structure. (You may calculate the appropriate integrals or estimate the relevant areas under the curve graphically.) Then recalculate the probabilities by approximating the integral as |Ψ(x0)|^2 ∆x, where x0 is evaluated in the middle of the range from x1 to x2.
Suppose that a molecular orbital has the (unnormalized) form 0.727A + 0.144B. Find a linear combination of the orbitals A and B that is orthogonal to this combination and determine the normalization constants of both combinations using S = 0.117. Show full and complete procedure, indicating where and how you are using the value of S
It is commonly the case that 2 energy states have the same energy. States at the same energy are known as degenerate. A given molecule has 2 degenerate states that are 700 cm-¹ (wavenumbers, 1/2) above the lowest energy state. Remember that E = h * v= h * C/ where c is the speed of light. a) Calculate the temperature at which this molecule has a 15% probability to be in either of the higher energy degenerate states. b) If you were able to observe this molecule for a 100 second time period, what would be the total amount of time you observe the molecule to be in the upper degenerate energy states and what would be the total amount of time you observe the molecule to be in the lower energy state? c) If there were 100 molecules present, on average about how many would be in the upper degenerate energy states and how many would be in the lower energy state?
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
determine 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)
Account physically for the fact that a linear polyatomic molecule composed of N atoms has one more vibrational mode than a non-l inear molecule of N atoms.
Iodine-124 as a salt can be used in positron emission tomography (PET) to image and monitorthe thyroid for cancer screening. Assume a rotating 1H124I molecule is a stationary iodine atomupon which hydrogen circulates in a plane 161 pm away. Calculate:a) the moment of inertia of the molecule b) the greatest wavelength of radiation (lowest energy radiation) that can rotationally excite themolecule.
a) What terms can arise from the (He)2s22p13d1 excited configuration of carbon? Terms: b) What levels can the following terms possess:/ 1.5S 2.3F 3.5p
ClO2 is a nonlinear molecule with one unpaired electron. The ground-state has a B1 symmetry. The molecule has been trapped (immobilized) in a solid matrix, lying in the yz plane. Its electronic absorption spectrum showed an allowed transition when using light polarized in the y-direction. To what electronic state was the molecule excited? Justify your answer.
Calculate the energy levels of the 7-network in octatetraene, C3H10 (CC-C=C-C=C-C=C), using the particle in the box model. To calculate the box length, assume that the molecule is linear and use the values 135 and 154 pm for C=C and C-C bonds. What is the wavelength of light required to induce a transition from the ground state to the first excited state?