Answered: Confirm that the wavefunctions of the…

Science

Chemistry

Confirm that the wavefunctions of the 2D rigid rotor for m=1 and m=2 are orthogonal.

Physical Chemistry

2nd Edition

ISBN:9781133958437

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

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

Chapter12: Atoms And Molecules

Section: Chapter Questions

Problem 12.47E

See similar textbooks

Related questions

Q: Suppose that particle in two-dimensional (2D) box a a x; 30 V(xy) = x(а — х) у(b-у) (a³b5)i] Show…

A: We have the following two points from the question: The particle is in a 2D box The wave function…

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

Q: Evaluate the average potential energy, , for the ground state (u = 0) of the harmonic oscillator by…

A: The wave function which can be used for determining the expression for potential energy is shown…

Q: P11B.7 The microwave spectrum of 16O*CS gave absorption lines (in GHz) as follows: 1 3 4 325…

Q: Assume that the states of the π electrons of a conjugated molecule can be approximated by the…

A: SOLUTION: Step 1: For a particle in one dimensional Box, the normalized Wave function is

Q: The following parameters describe the electronic ground state and an excited electronic state of…

A: The bond length in electronically excited state is greater than that in ground state.

Q: Calculate the energies of the first four rotational levels of 1H127I free to rotate in three…

A: First determine the reduced mass of 1H127. Next calculate the, moment of inertia.

Q: Sketch the form of the wavefunctions for the harmonic oscillator with quantum numbers v = 0 and 1.…

A: Harmonic oscillator explains vibrational motion of particle. In quantum mechanical model, the…

Q: Locate the nodes of a harmonic oscillator wavefunction with v = 2. (Express your answers in terms of…

A: The vibrational energy levels are all equally spaced i.e. ΔE1=ΔE2

Q: The moment of inertia of an SF6 molecule is 3.07 × 10−45 kg m2. What is the minimum energy needed to…

A: Given: The moment of interia of an SF6 molecule is 3.07×10-45 kg m2.

Q: Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a…

A: The expectation value of x2 for a particle is given by following expression. The value of ψ for one…

Q: 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…

A: The answer for first question is given below. Kindly repost the other question as separate one

Q: For a certain harmonic oscillator of effective mass 2.88 × 10−25 kg, the difference in adjacent…

A: Given: Effective mass = 2.88 × 10−25

Q: Normalize the wavefunction, Y = Asin(2x),x = 0 to 2n. Refer to a table of integral if %D necessary.

Q: It is useful to define the spin angular momentum ladder operators or shift operators St=S, +iS, and…

A: Here we are required to prove the following relation

Q: How do the energy eigenstates of the 2D rigid rotor compare to (1) the eigenstates of a free…

Q: What is the dissociation energy, D (in kJ/mole) for this Morse oscillator?

Q: For a certain harmonic oscillator of effective mass 1.33 × 10−25 kg, the difference in adjacent…

Q: Consider the following two systems: (a) an electron in a onedimensional box of length 1.0 Å and (b)…

A: (a)For an electron in a 1-D box, the length of the box is: The energy of the n energy levels can be…

Q: Assume 1,3,5 -hexatriene to be a linear molecule and model the pi electrons as particles in a…

Q: Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the…

A: Normalization is the scaling of wave functions so that all the probabilities add to 1.

Q: Calculate the value of ml for a proton constrained to rotate in a circle of radius 100 pm around a…

A: Given, Radius of the circle = 100 pm =…

Q: Normalize (to 1) the wavefunction e-ax^2 in the range −∞ ≤ x ≤ ∞, with a > 0. Refer to the…

A: Given: The wavefunction is e-ax^2 The range is −∞ ≤ x ≤ ∞ and a > 0.

Q: Consider the diatomic molecule AB modeled as a rigid rotor (two masses separated by a fixed distance…

Q: 8. Do the linear momentum operator px and angular momentum operator Lx commute. Can the velocity in…

Q: What is the magnitude of the angular momentum of a CH4 molecule when it is rotating with its minimum…

A: Known details, The minimum energy to rotate = 2.11×10–22J Moment of Inertia is 5.27 × 10-47 kg m2

Q: Derive an expression for the force constant of an oscillator that can be modelled by a Morse…

Q: A particle of spin 1/2 and mass m moves subject to the Hamiltonian: P² 1 1 1 P² = +/-mw²X² + +=mw²y²…

Q: assuming that the vibrations of a 35Cl2 molecule are equivalent to those of a harmonic oscillator…

A: The answer is given as follows

Q: For a system consisting of three particles in 3D, on what variables does the time-independent wave…

Q: A hydrogen atom. treated as a point mass. is confined to a one-dimensional square well of width 1.0…

Q: Using the rigid rotor model, calculate the energies in Joules of the first three rotational levels…

A: Rotational energy (E) for one mole of HBr is calculated by equation (1) in which ‘h’ is the plank…

Q: (structure below) is proposed as a model compound for an application of the particle-in-a-ring…

Q: As noted in lecture, the rigid rotor model can be improved by recognizing that in a realistic…

A: The rotational constant B of HBr molecule is given to be 8.473 cm-1 while that of value of α is…

Q: For trans-1,3,5-hexatriene: State, giving reasons, appropriate values of n for the HOMO and the LUMO…

A: This is a quantum chemistry problem. System is 1,3,5-hexatriene.

Q: Evaluate the linear momentum and kinetic energy of a free proton described by the wavefunction e−ikx…

A: Wavefunction = e-ikx Where, k = 5 nm-1

Q: The normalized wavefunctions for a particle-in-box (length, a = 40 nm) in the x- direction are given…

A: Given wavefunction:

Q: 4 For the 1S 2P (Lyman a) transition in the hydrogen atom, evaluate the total integrated absorption…

Q: Give the term symbol(s) correspond to the ground state configuration of a Y2+ ion.

A: We have to determine the term symbol(s) correspond to the ground state configuration of a Y2+ ion.

Q: Suppose that the internuclear distance may be written R = Re + x where Re is the equilibrium bond…

A: Internuclear distance is the distance between the two metals. The internuclear distance is given by,…

Q: Assuming a harmonic potential, if the zero-point energy for a diatomic molecule is 861 cm1. What is…

A: Assuming harmonic potential,The vibrational energy, Ev=(v+12)ωe cm-1Zero-point energy (when v=0)…

Q: What are the dimensions of a wavefunction that describes a particle free to move in both the x and y…

A: The wave function t of the particle in a two-dimensional box is as follows:

Q: Consider a particle of mass m confined to a one-dimensional box of length L and in a state with…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 1. Calculate the wavelength and frequency at which the intensity of the radiation is a maximum for a…

A: The wavelength (λmax) of the maximum amount of radiation emitted by a black body at a certain…

Q: Calculate the separation between the two lowest energy levels for an N2 molecule in a one-…

A: Given, mass of N2, m = 28 amu = 28x1.6605x10-27 kg Length = 2 cm =…

Q: What is the speed of a photoelectron ejected from a molecule with radiation of energy 21 eV and…

A: the speed of photoelectron is measured applying this formula = E = 1/2 mv2

Q: Calculate the minimum excitation energy (i.e. the difference in energy between the first excited…

A: Given: To Calculate the minimum excitation energy Formula: The expression to calculate the minimum…

Q: P7E.6 Before attempting these calculations, see Problem P7E.5. The following data give the…

A: The force constant k is related to wavenumber ν- by using the formula ν-=12πckμ c is the speed of…

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

100%

Confirm that the wavefunctions of the 2D rigid rotor for m=1 and m=2 are orthogonal.

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

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 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?
Show that the normalization constants for the general form of the wavefunction =sin(nx/a) are the same and do not depend on the quantum number n.
Normalize (to 1) the wavefunction e-ax^2 in the range −∞ ≤ x ≤ ∞, with a > 0. Refer to the Resource section for the necessary integral.
Normalize (to 1) the wavefunction e–ax in the range 0 ≤ x ≤ ∞, with a > 0.
What are the dimensions of a wavefunction that describes a particle free to move in both the x and y directions?
Without evaluating any integrals, state the value of the expectation value of x for a particle in a box of length L for the case where the wavefunction has n = 2. Explain how you arrived at your answer.
Determine the number and location of the maxima in the plot r2R*(r) R(r) for the 2s wavefunction.
A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.
Normalize the wave function ψ= A sin (nπ/a x) by finding the value of the constant A when the particle is restricted to move in one dimensional box of width ‘a’.
Evaluate the linear momentum and kinetic energy of a free proton described by the wavefunction e−ikx with k = 5 nm−1.
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.
Calculate the expectation values of x and x2 for a particle in the state with n = 1 in a one-dimensional square-well potential.