Physical Chemistry Problem: Evaluate the average z-component of the angular momentum of a particle on a...
Physical Chemistry Problem:
Evaluate the average z-component of the angular momentum of a particle on a ring that is described by the (unnormalized) wavefunctions (a) e^–2iψ, (c) cos ψ, and (c) (cos χ)e^iψ + (sin χ)e^–iψ. (note - cos χ and sin χ are just weighting coefficients, ie constants)
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Physical Chemistry Problem:
Evaluate the average z-component of the angular
momentum of a particle on a...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
A particle on a sphere is described by the state function Ψ = N {1 +...
A particle on a sphere is described by the state function Ψ = N {1 + cos(θ)} Find a) the value of the normalization constant N b) the expectation value of the energy E c) the possible values of the z component of angular momentum (Lz) that might be measured, and which of these possibilities is most likely.
Problem 1. Determine the angular momentum, the z-component of the angular momentum, and the energy of...
Problem 1. Determine the angular momentum, the z-component of the angular momentum, and the energy of the rigid rotor in states defined by the following spherical harmonics (the moment of inertia is "1"): a) Yoo b) 722 c) V2.2 d) Y105
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2...
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in a ring for m-l and m--1 are, respectively N2T where ? is the angular position of the particle relative to thex axis (see slide 15 of lecture 74a). (a) show that the probability density does not depend on 0. (b) Show that P,(o)-sin() where p, (0) rticle in the quantum state V, (d) p, (0) obviously resembles one of the orbitals of the is...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20...
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2. (a) (7pt) A wavefunction is given by y, (e, 4-B sin cos(6). Can this function be an eigenfunction of Legendrían operator (A2.sunagatsineaesin暘for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and...
Problem 11.36 Ok m/s. Determine the angular momentum of a 77-g particle about the origin of...
Problem 11.36 Ok m/s. Determine the angular momentum of a 77-g particle about the origin of coordinates when the particle is at 3 = 4.4 m, y = -6.2 m, and it has velocity v= Find the c-component. Express your answer using two significant figures. Lx = 3.8 kg . m/s Submit Previous Answers Answer Requested Part B Find the y-component. Express your answer using two significant figures. I A m O 2 ? Ly = 30.36 kg. m/s Submit...
4. Answer the following short answer questions. a. For the particle in a square well, when...
4. Answer the following short answer questions. a. For the particle in a square well, when solving Schrödinger equation in all regions, one gets the following wavefunctions (where A,B,C,D,F, and G are constants): 4.(x) = Ce** + De-*** (x) = A cos Bx + B sin Bx m(x) = Fe*:* + Ge-*** where Region 1/2 [2m(V. - E) (2mE ki and B = Since there are six unknown constants, one needs six boundary conditions/constraints to complete the problem. State the...
Parts B, C D, E Rules for Orbital Angular Momentum Constants Periodic Table Part A Learning...
Parts
B, C D, E
Rules for Orbital Angular Momentum Constants Periodic Table Part A Learning Goal How many different values of I are possible for an electron with principal quantum number n Express your answer as an integer To understand and be able to use the ruiles for determining allowable orbital angular momentum states 52 Several numbers are necessary to describe the states available to an electron in the hydrogen atom. The principal quantum number n determines the energy...
(V.4) A particle is observed to have orbital angular momentum quantum number 2. The z component of the angular momentum is measured to be Lz2h. A second particle is observed to have orbital angular momentum quantum number l2-2 and a z component ha = +2 V1(1 +1), what are the possible outcomes, and with what relative probabilities? What is the expectation value (L)'? h. If a measurement is made of the total angular momentum L-h
Problem 1. Determine the angular momentum, the z-component of the angular momentum, and the energy of the rigid rotor in states defined by the following spherical harmonics (the moment of inertia is "1"): a) Yoo b) 722 c) V2.2 d) Y105
Question #2: 6 pts] Find the eigenvalues and the normalized eigenvectors of the matrix 21 2 -1 2 Question #3: 10 pts] The electron in a hydrogen atom is a linear combination of eigenstates. Let us assume a limited linear combination to provide some sample calculations $(r, θ, φ) 2 ,1,0,0 + '2,1,0 (a) Normalize the above equation. (b) What are the possible results of individual measurements of energy, angular momentum, and the z-component of angular momentum? (c) What are...
1. The wavefunction corresponding to Im> energy and angular momentum eigenstate of a particle rotating in a ring for m-l and m--1 are, respectively N2T where ? is the angular position of the particle relative to thex axis (see slide 15 of lecture 74a). (a) show that the probability density does not depend on 0. (b) Show that P,(o)-sin() where p, (0) rticle in the quantum state V, (d) p, (0) obviously resembles one of the orbitals of the is...
322 CHAPTER 5. ANGULAR MOMENTUM Problem 5.12 Consider a particle whose wave function is 1 222-x2-y2 4 A 3 xz (x, y, z) = 2 2 Calculate L2 (x, y, z) and L-y(x, y, z). Find the total angular momentum of this particle. (b) Calculate L+ y (x, y, z) and (Y L+ W). (c)If a measurement of the z-component of the orbital angular momentum is carried out, find the probabilities corresponding to finding the results 0, h, and -h....
5. Part 1. (6 pt) An electron moves around a 2D ring with ring radius 0.50 nm in the state m --20. Determine the wavelength (in nm) of the particle wave induced by this electron. (similar to a question in Exam 1) Part 2. (a) (7pt) A wavefunction is given by y, (e, 4-B sin cos(6). Can this function be an eigenfunction of Legendrían operator (A2.sunagatsineaesin暘for a quantum particle moving around a spherical surface)? If so, determine the eigenvalue and...
Problem 11.36 Ok m/s. Determine the angular momentum of a 77-g particle about the origin of coordinates when the particle is at 3 = 4.4 m, y = -6.2 m, and it has velocity v= Find the c-component. Express your answer using two significant figures. Lx = 3.8 kg . m/s Submit Previous Answers Answer Requested Part B Find the y-component. Express your answer using two significant figures. I A m O 2 ? Ly = 30.36 kg. m/s Submit...
4. Answer the following short answer questions. a. For the particle in a square well, when solving Schrödinger equation in all regions, one gets the following wavefunctions (where A,B,C,D,F, and G are constants): 4.(x) = Ce** + De-*** (x) = A cos Bx + B sin Bx m(x) = Fe*:* + Ge-*** where Region 1/2 [2m(V. - E) (2mE ki and B = Since there are six unknown constants, one needs six boundary conditions/constraints to complete the problem. State the...
Parts
B, C D, E
Rules for Orbital Angular Momentum Constants Periodic Table Part A Learning Goal How many different values of I are possible for an electron with principal quantum number n Express your answer as an integer To understand and be able to use the ruiles for determining allowable orbital angular momentum states 52 Several numbers are necessary to describe the states available to an electron in the hydrogen atom. The principal quantum number n determines the energy...
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