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1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orb...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
A hydrogen atom is in the n = 6 state. Determine, according to quantum mechanics, (a)...
A hydrogen atom is in the n = 6 state. Determine, according to quantum mechanics, (a) the total energy (in eV) of the atom, (b) the magnitude of the maximum angular momentum the electron can have in this state, and (c) the maximum value that the z component Lz of the angular momentum can have.
PLEASE COMPLETE B) and stay tuned for my following 2 questions where I will ask part c) and d). P...
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
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 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be ...
Problem 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
solution please An electron in an atom is in the 4Fs/2 state. (a) What are the...
solution please
An electron in an atom is in the 4Fs/2 state. (a) What are the values of the quantum numbers n, e, and j. (b) What is the magnitude IJI of the electron's total angular momentum in terms of h? (Show your work below.) (c) What are the possible values for the z component of the electron's total angular momentum in terms of h? mi F
2. (8 points) Consider an electron in a hydrogen atom with 1. There are three possible...
2. (8 points) Consider an electron in a hydrogen atom with 1. There are three possible eigen- states of the operator L2, given by 11, m) 11,1), 11,0), and 11,-1). (a) Recall that the raising/lower operators are given by L±-L, ±ill. Also recall the rela- tionship Use this relationship to determine the 3x3 matrix representation of Ly (using a basis com- prised of eigenstates of L). (b) What are the eigenvalues and associated eigenstates of the operator Ly? (c) If...
An electron in the Hydrogen atom is in the excited state with energy E2. a) According...
An electron in the Hydrogen atom is in the excited state with energy E2. a) According to the Bohr model, what is the radius of the atom in this state, in Angstroms? b) What is the wavelength le of the electron, in Angstroms? c) What is the momentum of the electron, in kg-m/s ? d) This atom decays from the excited state with energy E2 to the ground state with energy E1 . What is the energy of the emitted photon?...
Consider the hydrogen atom and its eigenstates, omitting any effects of fine structure (spin- orbit coupling). For the state y21-1 give the a. expectation value of the energy b. c. expectation value of the z-component of the orbital angular momentum d. expectation value of the y-component of the orbital angular momentum e. Now replace the electron with a muon which has a mass mu200 me. What is the ratio expectation value of the total orbital angular momentum of the ground...
The function ψ2px-1(ψ2,1,1+ψ2,1-1) describes an electron in the 2px state of a hydrogen-like atom (with unspecified spin). Functions ψη..my are normalized egenfuntions of the energy operator (A), the square of angular momentum operator (12), and the z-component of angular momentum operator (Lz), that is 4. E1 a) Show that the function ψ2px is an eigen function of both the energy operator and the square of angular momentum operator. Find the corresponding eigenvalues. b) Determine the expected value and the uncertainty...
PLEASE COMPLETE B) and stay tuned for my
following 2 questions where I will ask part c) and d). Part a) has
already been posted.
The lowest energy state of a hydrogen-like atom has total angular momentum J-1/2 (from the l-O orbital angular momentum and the electron spin s 1/2). Furthermore, the nucleus also has a spin, conventionally labeled I (for hydrogen, this is the proton spin, 1 1/2). This spin leads to an additional degeneracy. For example, in the...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
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 7.49
Problem 7.49 A hydrogen atom is placed in a uniform magnetic field Bo Bo (the Hamiltonian can be written as in Equation 4.230). Use the Feynman-Hellman theorem (Problem 7.38) to show that a En (7.114) where the electron's magnetic dipole moment10 (orbital plus spin) is Yo l-mechanical + γ S . μ The mechanical angular momentum is defined in Equation 4.231 a volume V and at 0 K (when they're all in the ground state) is41 Note: From...
solution please
An electron in an atom is in the 4Fs/2 state. (a) What are the values of the quantum numbers n, e, and j. (b) What is the magnitude IJI of the electron's total angular momentum in terms of h? (Show your work below.) (c) What are the possible values for the z component of the electron's total angular momentum in terms of h? mi F
2. (8 points) Consider an electron in a hydrogen atom with 1. There are three possible eigen- states of the operator L2, given by 11, m) 11,1), 11,0), and 11,-1). (a) Recall that the raising/lower operators are given by L±-L, ±ill. Also recall the rela- tionship Use this relationship to determine the 3x3 matrix representation of Ly (using a basis com- prised of eigenstates of L). (b) What are the eigenvalues and associated eigenstates of the operator Ly? (c) If...
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