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![AS, S₂ îis Haf 3, 5 5.5 - 6+3)(5+5) = 5,2+52 +2575 3.-5, - 52-52-53 Hung A [$$_3?] sa 2 S(5+1) <33 <s,2) <s27 = S, (5,+1) ħ2](http://img.homeworklib.com/questions/050748a0-e500-11ea-8213-517b541b018f.png?x-oss-process=image/resize,w_560)
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Consider a hydrogen atom in its ground state. The hyperfine interaction between the magnetic moment of...
11.17 A positronium atom is a hydrogen-like atom with a positron (m = meq = te,...
11.17 A positronium atom is a hydrogen-like atom with a positron (m = meq = te, spin 1/2) as a nucleus and a bound electron. The hyperfine structure in the ground state of positronium is described by a perturbation Hamiltonian H' = AS, S/hwhere S, are the spins of the elec- tron and positron. a) What is the Bohr energy of the ground state of positronium (ignore hyperfine structure for now)? b) The electron and positron spins can be coupled...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht f...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
9. An electron moving with non-relativistic velocity v in an electric field E experiences a magnetic...
9. An electron moving with non-relativistic velocity v in an electric field E experiences a magnetic fieldB given by: v x (-V(r)) v x E B=- where (r) is the electric potential. This magnetic field interacts with the magnetic moment u of the electron given by -S, =n me where S is the electron spin. Assuming non-relativistic mechanics, show that the Hamiltonian representing this effect (spin-orbit coupling) for a spherically-symmetric electric potential is: 1 dφ(r) S.L ΔΗ [6] r dr...
Question 1: Consider the following situation: For the hydrogen atom in its ground state pictured on...
Question 1: Consider the following situation: For the hydrogen atom in its ground state pictured on the right, classically orbiting at the Bohr Radius 20 = 5.29 + 10-11m, calculate: a) The speed the electron is traveling at. b) The angular momentum 1 =7 x 5 of the electron. Compare it to = 1.055 10-34J.s. c) The magnetic field due to the electron at the position of the proton. Is it into the page or out of the page? on-...
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...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
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...
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...
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...
11.17 A positronium atom is a hydrogen-like atom with a positron (m = meq = te, spin 1/2) as a nucleus and a bound electron. The hyperfine structure in the ground state of positronium is described by a perturbation Hamiltonian H' = AS, S/hwhere S, are the spins of the elec- tron and positron. a) What is the Bohr energy of the ground state of positronium (ignore hyperfine structure for now)? b) The electron and positron spins can be coupled...
Tl 6. (4 pts) We calculated Ahf for the ground state Hydrogen atom, but now let us consider Hht for the ground state of the deuterium atom. The basic idea is the same: Here the matrix representation of S is the same, since it represents the spin operator for the spin- electron, but that of 7 is different because the deuteron is a spin-1 particle (neutron+proton) whose spin has 3 possible values for the magnetic quantum number. Also, we must...
9. An electron moving with non-relativistic velocity v in an electric field E experiences a magnetic fieldB given by: v x (-V(r)) v x E B=- where (r) is the electric potential. This magnetic field interacts with the magnetic moment u of the electron given by -S, =n me where S is the electron spin. Assuming non-relativistic mechanics, show that the Hamiltonian representing this effect (spin-orbit coupling) for a spherically-symmetric electric potential is: 1 dφ(r) S.L ΔΗ [6] r dr...
Question 1: Consider the following situation: For the hydrogen atom in its ground state pictured on the right, classically orbiting at the Bohr Radius 20 = 5.29 + 10-11m, calculate: a) The speed the electron is traveling at. b) The angular momentum 1 =7 x 5 of the electron. Compare it to = 1.055 10-34J.s. c) The magnetic field due to the electron at the position of the proton. Is it into the page or out of the page? on-...
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...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
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...
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...
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...
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