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Problem 3. At some moment of time, an electron in the hydrogen atom is prepared in...
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...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
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...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a)...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a) Using the general raising and lowering operator formalism e.g Construct the linear combinations of mi ms states which have 2) j 5/2,my 3/2 3) j-3/2, m,-3/2 (b) An external magnetic field B is applied in the z-direction. The interaction between the external field and the magnetic moment of the electron is given by Hmag_ 2mc Find the energy splitting induced between the states (1)...
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...
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...
PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes transition from...
PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes transition from n=4 to n=2. A. Find the energy of the emitted radiation (photon) in this transition in ev. B. Find the wave length, frequency, and its De Broglie momentum. C. Can you make a guess of the color of this photon? D. FOR THE ELECTRON IN n= 2 CALCULATE ITS SPEED, RADIUS FROM THE NUCLUS, LINEAR MOMENTUM, ANGULAR MOMENTUM, KINETIC ENERGY, TOTAL ENERGY, AND De...
A-D Please PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes...
A-D Please
PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes transition from n-4 to n-2. A. Find the energy of the emitted radiation (photon) in this transition in ev. B. Find the wave length, frequency, and its De Broglie momentum. C. Can you make a guess of the color of this photon? D. FOR THE ELECTRON IN N= 2 CALCULATE ITS SPEED, RADIUS FROM THE NUCLUS, LINEAR MOMENTUM, ANGULAR MOMENTUM, KINETIC ENERGY, TOTAL ENERGY,...
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...
1. Given a state y(r) expanded on the eigenstates of the Hamiltonian for the electron, H, in a hydrogen atom: where the subscript of E is n, the principal quantum number. The other two numbers are the 1 and m values, find the expectation values of H (you may use the eigenvalue equation to evaluate for H), L-(total angular momentum operator square), Lz (the z-component of the angular momentum operator) and P (parity operator). Draw schematic pictures of 1 and...
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...
(VI) Hydrogen atom A What is the probability that an electron in the ground state of hydrogen will be found inside the nucleus? Find the expression for the probability, in which Rc denotes the the radius of nucleus. Hints: Rc IT 127 i) Integration in spherical coordinate system (r, 0, 0)|r2 sin Ododedr Jo Jo Jo 2.c 20 e Jo a 2 B Construct the wavefunction for an electron in the state defined by the three quantum numbers: principal n...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a) Using the general raising and lowering operator formalism e.g Construct the linear combinations of mi ms states which have 2) j 5/2,my 3/2 3) j-3/2, m,-3/2 (b) An external magnetic field B is applied in the z-direction. The interaction between the external field and the magnetic moment of the electron is given by Hmag_ 2mc Find the energy splitting induced between the states (1)...
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...
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...
PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes transition from n=4 to n=2. A. Find the energy of the emitted radiation (photon) in this transition in ev. B. Find the wave length, frequency, and its De Broglie momentum. C. Can you make a guess of the color of this photon? D. FOR THE ELECTRON IN n= 2 CALCULATE ITS SPEED, RADIUS FROM THE NUCLUS, LINEAR MOMENTUM, ANGULAR MOMENTUM, KINETIC ENERGY, TOTAL ENERGY, AND De...
A-D Please
PROBLEM #6. In BALMER lines in Hydrogen atom in Bohr model. An electron makes transition from n-4 to n-2. A. Find the energy of the emitted radiation (photon) in this transition in ev. B. Find the wave length, frequency, and its De Broglie momentum. C. Can you make a guess of the color of this photon? D. FOR THE ELECTRON IN N= 2 CALCULATE ITS SPEED, RADIUS FROM THE NUCLUS, LINEAR MOMENTUM, ANGULAR MOMENTUM, KINETIC ENERGY, TOTAL ENERGY,...
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