Homework Answers
This is a straightforward problem but we have to be careful as some complex calculations are involved. First we have to find Hamiltonian matrix.For this we need Lx, Ly and Lz. You will be familiar about this. After that we will find eigenvalues of that matrix which will give us energy spectrum.
![Page 1) We have to have to find energy find energy spectrum. It means eigenvalues for - Ĥ= MEB So H= f [LxBx + Ly Byt Lz Bz]](http://img.homeworklib.com/questions/c7c84810-59df-11eb-aed9-7bff69d62184.png?x-oss-process=image/resize,w_560)
Hope this helps.Sorry for any calculation mistake.Have a nice day :)
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4. An atom with orbital angular momentum 1=1 is subject to a constant magnetic field B...
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)...
The orbital quantum number 1 determines the (a) direction of the electron's orbital angular momentum, (b)...
The orbital quantum number 1 determines the (a) direction of the electron's orbital angular momentum, (b) z-component of the electron's angular momentum, (c) magnitude of the electron's spin, (d) magnitude of the electron's orbital angular momentum.
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...
Parts B, C D, E Rules for Orbital Angular Momentum Constants Periodic Table Part A Learning...
Parts
B, C D, E
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Problem 5 a) An klectron in a Hydrogen atom moves around in a angular momentum. At...
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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...
qm 2019.3 3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with...
qm 2019.3
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Which of the following statements is TRUE? The angular momentum quantum number (1) describes the orientation...
Which of the following statements is TRUE? The angular momentum quantum number (1) describes the orientation of the orbital. The magnetic quantum number (mi) describes the size and energy associated with an orbital. The principal quantum number (n) describes the shape of an orbital. O An orbital is the path that an electron follows during its movement in an atom. The spin quantum number (ms) describes the orientation of the spin of the electron.
task: (a) Check that it meets the vector potential condition , where B is a constant...
task:
(a) Check that it meets the vector potential
condition , where B is a constant magnetic
field.
(b) Let A be the vector potential given under (a). Show that he is
a member
occurring in the Hamilotonian for a particle in the EM field equal
to the expression for the interaction of the magnetic moment
μL
due to the orbital angular momentum with the magnetic field B
where q is the charge and a m is the mass of...
10.28 Using equation 10.55, calculate the difference in energy between the two spin angular momen...
10.28 Using equation 10.55, calculate the difference in energy between the two spin angular momentum states of a hydrogen atom in the 1s orbital in a magnetic field of 1 T. What is the wave- length of radiation emitted when the electron spin "flips"? In what region of the electromagnetic spectrum is this? The energy of the spin magnetic moment in a magnetic field B is (see equation 10.41) (10.55)
10.28 Using equation 10.55, calculate the difference in energy between...
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)...
The orbital quantum number 1 determines the (a) direction of the electron's orbital angular momentum, (b) z-component of the electron's angular momentum, (c) magnitude of the electron's spin, (d) magnitude of the electron's orbital angular momentum.
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...
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...
Problem 5 a) An klectron in a Hydrogen atom moves around in a angular momentum. At what frequency does the electron revolve in the magnctic field? circular orbit of radius 0 52 x 100 m. Suppose the hydrogen atom is transported into a magnetic field of 0.20 T, where the magnetic field is parallel so the orbial Subit Anawer Tries 0/6 b) What is the associated speed of the electroe? Assume that the radius of the orbit remains constant Subit...
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...
qm 2019.3
3. The Hamiltonian corresponding to the magnetic interaction of a spin 1/2 particle with charge e and mass m in a magnetic field B is À eB B. Ŝ, m where Ŝ are the spin angular momentum operators. You should make use of expres- sions for the spin operators that are given at the end of the question. (i) Write down the energy eigenvalue equation for this particle in a field directed along the y axis, i.e. B...
Which of the following statements is TRUE? The angular momentum quantum number (1) describes the orientation of the orbital. The magnetic quantum number (mi) describes the size and energy associated with an orbital. The principal quantum number (n) describes the shape of an orbital. O An orbital is the path that an electron follows during its movement in an atom. The spin quantum number (ms) describes the orientation of the spin of the electron.
task:
(a) Check that it meets the vector potential
condition , where B is a constant magnetic
field.
(b) Let A be the vector potential given under (a). Show that he is
a member
occurring in the Hamilotonian for a particle in the EM field equal
to the expression for the interaction of the magnetic moment
μL
due to the orbital angular momentum with the magnetic field B
where q is the charge and a m is the mass of...
10.28 Using equation 10.55, calculate the difference in energy between the two spin angular momentum states of a hydrogen atom in the 1s orbital in a magnetic field of 1 T. What is the wave- length of radiation emitted when the electron spin "flips"? In what region of the electromagnetic spectrum is this? The energy of the spin magnetic moment in a magnetic field B is (see equation 10.41) (10.55)
10.28 Using equation 10.55, calculate the difference in energy between...
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