Answered: H.W. of lect. 11 For Harmonic…

H.W. of lect. 11 For Harmonic Oscillator, prove that the Sommerfeld quantization condition is given as equation described in the attachment below (in detailed

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter14: Rotational And Vibrational Spectroscopy

Section: Chapter Questions

Problem 14.62E

See similar textbooks

Related questions

Q: Why is a three-level laser less efficient than a four-level laser? Explain why the position of the…

A: Four level laser system has many advantages over 3 layer laser system. Three level layer operate in…

Q: It is 215K. If you know that the Debye temperature of silver is D, then the maximum frequency of the…

A: In Debye theory, the Debye temperature (θD) is the temperature of a crystal's highest normal mode of…

Q: An electronic vertical transition for a molecule is described in the following diagram. Based on…

A: Given electronic vertical transition:

Q: C) Write a Hamiltonian function representing an electron in the presence of a stationary positive…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: oues- Radiant energy Varies indirectly withiahy a Speed frepueney Dwaveleongth फणगळण of there. none

Q: Show me the complete Harmonic Oscillator System for the first three levels. Include all pertinant…

A: For a harmonic oscillator, the energy is quantized and the energy levels are equally spaced.

Q: Explain the iterative method for solving the single particle equations of the Kohn-Sham method for…

A: Answer - The Kohn–Sham equation is the one-electron Schrödinger equation (more clearly,…

Q: Use the conservative of mass interactive

Q: For a quantum mechanical harmonic oscillator, i) calculate the expectation value of the potential…

A: Answer - Quantum mechanical harmonic oscillator - The quantum harmonic oscillator is the…

Q: What is the amplitude and period of the function shown below?

A: Amplitude is maximum displacement from mean position. So in above wave amplitude is of 4 units…

Q: What are differences between n→π* and π →π* bonding electron transition in Fluorescence? Please…

A: Absorption spectroscopy of organic compounds is generally based on n→π* and π→π* bonding electron…

Q: energy

A: This question is related to fluorescence.

Q: How can you convert the wavelength to wave number and absorbance to transmittance?

Q: Describe how the profile of a radial distribution function graphs relate to planar and radial nodes.

A: The probability of finding a particle at a certain distance away from a tagged particle that enables…

Q: The first excited state of Cl- ion will have degeneracy of ..

A: The atomic number of Cl is 17 Hence the electronic configuration for the Cl is [Cl] =…

Q: The electronic spectra in the visible range span is __________

A: The visible light spectrum is the segment of the electromagnetic spectrum that the human eye can…

Q: schrodlinger Equation with fuep ding rom And its Application Deriv ation wave Explaynation and

A: Derivation of Schrodinger's wave equation/and its application:

Q: Write the Hamiltonian for the As atom. Use summation notation and specify limits

A: Hamiltonian is the Hamiltonian operator representing the energy of the electrons and nuclei in a…

Q: Compare and contrast the components of an infrared spectrophotometer with that of a visible…

A: From given Components of UV and IR spectrophotometer is compared and explained in detail as follows…

Q: Why does the fluorescence quenching happen? Please shortly answer at your own words. Answer should…

A: A molecule of a substance after absorbing UV/Vis light gets excited to upper energy level from the…

Q: disscus the concept of fluorescence and fluorescence quenching using relevant equations

A: When a system absorbs radiant energy and emits it instantaneously (within ~10-8 s )in the form of…

Q: Determine the value of x at which the first excited wave function of the harmonic oscillator…

A: Given that First excited wave function

Q: b) Predict the microstate table for the s'd' configuration. Assign the ground state term symbol.

A: Microstates are the different arrangements in which the electron can exist in their shells.

Q: schrodingen Equation wit, fuep and dingram Deviv ation wave Expoynationn And its Application

A: You have multiple questions, so I will solved first question for you and please post separately rest…

Q: Let's see how well the solution to the one-dimensional particle in a box Schrödinger equation…

A: The energy of a particle present in a one dimensional box of length a is given by the following…

Q: ⇒ Find Rydberg constant for and find for hydrogen atoms. an infinitely mossice nucleus

A: we know that:- Charge on the electron is given by= e = 1.6 ×10-19 C Mass of an electron is given…

Q: What is/are the limitation/s of the 200-400nm wavelength/

A: UV spectrophotometer has a range from 200nm to 400nm. We have been asked to state the limitations at…

Q: I am not sure on the steps to solve for cwsat.

Q: A He-Ne laser has a gas discharge temperature of 400 k. The atomic mass of Ne (which is responsible…

A: Solution- We’ve treated the spectra of light emitted by atoms transitioning between states E2 and E1…

Q: Calculate the ratio of sodium atoms in the 3p excited states to the number in the ground state at…

Q: The normalized wave function for a particle enclosed in a potential box of width a in the ground…

Q: Derive Schrodinger equation? Write its application to particle in one dimensional x. Also prove that…

A: The Eigen value equations and Eigen functions are used in the quantum mechanical derivation of…

Q: Why is emission energy lower than absorption energy? Please answer shorty at your own words. Answer…

A: Emission occurs when electrons return to their energy levels. Absorption occurs when electrons jump…

Q: Include the infrared data for the products in separate tables (experimental wavelength, literature…

Q: isible spectrum is in the 00-700 range, and contains abbut 40% 8f the sun's radiation intensity.…

A: The visible spectrum is the certain portion occupied electromagnetic spectrum and this visible…

Q: For scanning, the wavelength range is selected from 400 nm to 200 nm with medium scanning speed…

A: If the excitation is decided at 330 nm, then the wavelength range should start from 330+10 = 340 nm…

Q: u are provided sample solutions containing the following compounds, but in each case, there is some…

A: As per Bartle by guideline I am allowed to answer one question at a time.

Q: What is could be the calculated lambda max of this compound?

Q: Please help me with this. I will immediately give you a thumb up. Thank you so much! briefly…

A: In a hydrogen atom (single electron system), the energy of the electron can be best explained by the…

Q: What is difference between realtive and absolute configuration? Give example in each case.

A: An absolute configuration can be defined as the spatial arrangement of atoms of a compound, that are…

Q: The cyclobutadienyl cation (C4H4+) may be treated using the Huckel MO approach. The roots to the…

A: The energy of cyclobutadienyl cation (C4H42+) is needed to be determined using the Huckel MO…

Q: Assume an electron is trapped in the 2D potential well with length 200pm and width 450pm. Calculate…

A: In the question we are given, an electron trapped in a 2D potential well Length of 2D well, lx =…

Q: wavenumbers, D= -

A: Energy of photon is calculated by using photon quanta theory which states that energy comes in small…

Q: (a) Suppose that the you measure the lowest-energy rotational transition for 160'H at a frequency of…

A: 16O1H is a diatomic molecule for which the rotational energy is given as: E=BJ(J+1)

Concept explainers

Techniques and applications of quantum theory

Quantum theory, often known as quantum physics, is the foundation of modern physics and encompasses the nature and behavior of matter and energy at the atomic and molecular levels. As the exact nature and behavior of atomic and subatomic particles are impossible to determine, the laws of classical physics do not apply to this discipline. As a result, quantum field theory is primarily based on assumptions and probabilities.

Question

۲۸: ص
+ O U A A Fi
دبلا عنوان<
>
H.W. of lect. 11
For Harmonic Oscillator,
prove that the Sommerfeld
quantization condition is given
as equation described in the
attachment below (in detailed
steps);
$pxdx = 2n²v•mx?
A
المزید
مشاركة
النص
متحس س
ملاحظة

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Techniques and Applications of Quantum Theory

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

For a particle in a state having the wavefunction =2asinxa in the range x=0toa, what is the probability that the particle exists in the following intervals? a x=0to0.02ab x=0.24ato0.26a c x=0.49ato0.51ad x=0.74ato0.76a e x=0.98ato1.00a Plot the probabilities versus x. What does your plot illustrate about the probability?
Consider the following two systems: (a) an electron in a onedimensional box of length 1.0 Å and (b) a helium atom in acube 30 cm on an edge. Calculate the energy differencebetween ground state and first excited state, expressing youranswer in kJ mol-1.
The Li2+ ion is a hydrogenic atom. Calculate the valueof the Rydberg constant for Li2+. By what factor does it differfrom the Rydberg constant for atomic hydrogen?
Bohr’s model can be used for hydrogen-like ions—ions thathave only one electron, such as He + and Li2 + . (a) Why isthe Bohr model applicable to He + ions but not to neutral Heatoms? (b) The ground-state energies of H, He + , and Li2 + aretabulated as follows:By examining these numbers, propose a relationship betweenthe ground-state energy of hydrogen-like systems and thenuclear charge, Z. (c) Use the relationship you derive in part(b) to predict the ground-state energy of the C5 + ion.
Bohr’s model can be used for hydrogen-like ions—ions thathave only one electron, such as He + and Li2+ . (a) Why isthe Bohr model applicable to He + ions but not to neutral Heatoms? (b) The ground-state energies of H, He + , and Li2 + aretabulated as follows: By examining these numbers, propose a relationship betweenthe ground-state energy of hydrogen-like systems and thenuclear charge, Z. (c) Use the relationship you derive in part(b) to predict the ground-state energy of the C5+ ion.
Using the rigid rotor model, calculate the energies in Joules of the first three rotational levels of HBr, using for its moment of inertia I = μR2, with μ = mHmX/(mH + mX) and equilibrium internuclear distance = 1.63 Å. To put these energies into units that make sense to us, convert energy to kJ/mol. (Simply estimate atomic masses from the average atomic weights of the elements given in the periodic table).
What configurations must undergo the distortions predicted by the Jahn-Teller theorem? Why is distortion at eg level greater than at t2g?
Describe and justify the Born interpretation of the wavefunction.
Discuss how to derive diatomic term symbols e.g N2 and what do the + and - signs over terms mean.
8C.4 (a) the moment of inertia of a CH4 molecule is 5.27 x 10^-47 kg m^2. What is the minimum energy needed to start it rotating? 8C.5 (a) use the data in 8C.4 (a) to calculate the energy needed excite a CH4 molecule from a state with l=1 to a state with l=2
Calculate the energies of the first four rotational levels of 1H127I free to rotate in three dimensions; use for its moment of inertia I = μR2, with μ = mHmI/(mH + mI) and R = 160 pm. Use integer relative atomic masses for this estimate.
Calculate the value of ml for a proton constrained to rotate in a circle of radius 100 pm around a fixed point given that the rotational energy is equal to the classical average energy at 25 degrees C. (Mass of a proton = 1.6726 x 10^-27 kg, classical average energy=1/2kBT, where kBT is Boltzman constant = 1.30 x 10^ -23 J K^-1, and T is the temperature.)