None 4. The harmonic oscillator only works for parabolic potentials, but true potentials are of course anharmonic.Consider the anharmonic potential that gives the energy levels with the following expression:E₁ =159.12(v+0.5)-0.725(v+0.5)- 0.0011(v+0.5)³Determine the vibrational quantum number Vmax at which the vibrational level spacing vanishes, andestimate the dissociation energy Do. The known dissociation energy is Do=0.73 eV. How well does thisanharmonic potential represent the true potential?

Answered: Image /qna-images/answer/d9bbb686-3acd-48f2-8d20-5173920c92d3.jpg

Answered: 4. The harmonic oscillator only works…

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

We can use the classical harmonic oscillator to think about molecular bonds. The HCI molecule has a force constant k = 481 N/m. For the mass, use the reduced mass, which is defined as µ = (m₁m₂)/(m₁+m₂). a) Plot the potential energy of HCl from -1 to 1 Å. What happens to the curvature of the potential as the force constant is varied? What does this mean physically? b) Plot position as a function of time for a total energy of 6 x 10-20 J. What is the period of the motion? How does the period change as the force constant is varied? Explain why this makes sense physically.
As noted in lecture, the rigid rotor model can be improved by recognizing that in a realistic anharmonic potential, the bond length increases with the vibrational quantum number v. Thus, the rotational constant depends on v, and it can be shown that By = Be – ae(v +). For 'H®Br, B = 8.473 cm1 and a = 0.226 cm². Use this information to calculate the bond length for HBr a) as a rigid rotor, and b) as a nonrigid rotor in the ground vibrational state. Find a literature value for this bond length (cite your source) and compare your answers. Under what conditions would you expect the nonrigid rotor to be a significantly better model?
Assuming the vibrations of a ¹4N2 molecule are equivalent to those of a harmonic oscillator with a force constant kr = 2293.8 N/m, what is the zero-point energy of vibration of this molecule? Use m(14N) = 14.0031 mu.
Calculate the proportion of I2 molecules in their basal state, first and second excited state at 25 °C. The wave number is 214.6 cm−1 Hints: Equidistant levels, relation wave numbers and energy y (kT/hc) = 207.226 cm−1 2) At what temperature does the level ν = 1 of I2 have i) half of the population of the basal state, ii) the same population as the basic state? I need to understand and solve the second question
Light-induced degradation of molecules, also called photobleaching, is a serious problem in applications that require very high intensities. A molecule of a fluorescent dye commonly used to label biopolymers can withstand about 106 excitations by photons before light-induced reactions destroy its π system and the molecule no longer fluoresces. For how long will a single dye molecule fluoresce while being excited by 1.0 mW of 488 nm radiation from a continuous-wave laser? You may assume that the dye has an absorption spectrum that peaks at 488 nm and that every photon delivered by the laser is absorbed by the molecule.
Calculate the proportion of I2 molecules in their basal state, first and second excited state at 25 °C. The wave number is 214.6 cm−1 Hints: Equidistant levels, relation wave numbers and energy y (kT/hc) = 207.226 cm−1 a) At what temperature does the level ν = 1 of I2 have i) half of the population of the basal state, ii) the same population as the basic 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
A diatomic Hydrogen (H2) molecule with a potential between its two Hydrogen atoms can be modelled using the Morse potential: V(x) = V0 e−αx (e−αx - 2), where α = 19.3 nm−1 and V0 = 4.52 eV. Assuming the H2 molecule has no rotational energy. Determine the minimum value of the Morse potential, V . (State in eV, to 3 s.f.)
Treat a vibrating HI molecule as a hydrogen atom oscillating towards and away from a stationary iodine atom. Given the force constant of the HI bond is 314 N m-1, calculate the vibrational frequency of the molecule.
. Suppose a system of 4 molecules has a total energy of Etot = 4(+) where the energy of each molecule can be in the range Co. Co+c, co + 2e, co + 3c, co + 4e. Find all possible configurations, calculate the weight of each, identify most probable configuration, and calculate the probability of observing the o state.
J.G. Dojahn et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. These anions have a 2Σu+ ground state and 2Πg, 2Πu, and 2Σg+ excited states. To which of the excited states are electric-dipole transitions allowed from the ground state? Explain your conclusion.
Assuming that the vibrations of a 35Cl2 molecule are equivalent to those of a harmonic oscillator with a force constant kf = 329 N m−1, what is the zero-point energy of vibration of this molecule? Use m(35Cl) = 34.9688 mu.

SEE MORE QUESTIONS

Recommended textbooks for you

Chemistry

ISBN:

9781305957404

Author:

Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:

Cengage Learning

Chemistry

ISBN:

9781259911156

Author:

Raymond Chang Dr., Jason Overby Professor

Publisher:

McGraw-Hill Education

Principles of Instrumental Analysis

Chemistry

ISBN:

9781305577213

Author:

Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:

Cengage Learning

Chemistry

ISBN:

9781305957404

Author:

Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:

Cengage Learning

Chemistry

ISBN:

9781259911156

Author:

Raymond Chang Dr., Jason Overby Professor

Publisher:

McGraw-Hill Education

Principles of Instrumental Analysis

Chemistry

ISBN:

9781305577213

Author:

Douglas A. Skoog, F. James Holler, Stanley R. Crouch

Publisher:

Cengage Learning

Organic Chemistry

Chemistry

ISBN:

9780078021558

Author:

Janice Gorzynski Smith Dr.

Publisher:

McGraw-Hill Education

Chemistry: Principles and Reactions

Chemistry

ISBN:

9781305079373

Author:

William L. Masterton, Cecile N. Hurley

Publisher:

Cengage Learning

Elementary Principles of Chemical Processes, Bind…

Chemistry

ISBN:

9781118431221

Author:

Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard

Publisher:

WILEY

SEE MORE TEXTBOOKS