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Problem 5 Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If spin-orbit coupling is considered, the state of the electron can be writ- ten as lj, m;). Give the values of the quantum numbers j and m; and determine the term symbol of the groundstate of the system. b) After excitation, the electron relaxes into the 3d' configuration. Deter- mine the term symbols of the new electron configuration. For each term symbol (level) that you find, determine: • The magnitude of the total angular momentum. The degeneracy of the level. c) Determine the magnitude (in J) of the splitting of the different levels of the 3d' configuration. Assume that hcĂ = 2.19 x 10-7- hcR, where R is the Rydberg constant and hcR is the Rydberg energy. d) The electron is in the lowest level of the 3d' configuration. Can the system relax to the 2p' 2Pa/2 level through emission of a photon?

Problem 5 Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If spin-orbit coupling is considered, the state of the electron can be writ- ten as lj, m;). Give the values of the quantum numbers j and m; and determine the term symbol of the groundstate of the system. b) After excitation, the electron relaxes into the 3d' configuration. Deter- mine the term symbols of the new electron configuration. For each term symbol (level) that you find, determine: • The magnitude of the total angular momentum. The degeneracy of the level. c) Determine the magnitude (in J) of the splitting of the different levels of the 3d' configuration. Assume that hcĂ = 2.19 x 10-7- hcR, where R is the Rydberg constant and hcR is the Rydberg energy. d) The electron is in the lowest level of the 3d' configuration. Can the system relax to the 2p' 2Pa/2 level through emission of a photon?

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Problem 5 Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If spin-orbit coupling is considered, the state of the electron can be writ- ten as lj, m;). Give the values of the quantum numbers j and m; and determine the term symbol of the groundstate of the system. b) After excitation, the electron relaxes into the 3d' configuration. Deter- mine the term symbols of the new electron configuration. For each term symbol (level) that you find, determine: • The magnitude of the total angular momentum. The degeneracy of the level. c) Determine the magnitude (in J) of the splitting of the different levels of the 3d' configuration. Assume that hcĂ = 2.19 x 10-7- hcR, where R is the Rydberg constant and hcR is the Rydberg energy. d) The electron is in the lowest level of the 3d' configuration. Can the system relax to the 2p' 2Pa/2 level through emission of a photon?
Transcribed Image Text:Problem 5 Consider an electron in the hydrogen atom. The electron is initially in the groundstate. a) If spin-orbit coupling is considered, the state of the electron can be writ- ten as lj, m;). Give the values of the quantum numbers j and m; and determine the term symbol of the groundstate of the system. b) After excitation, the electron relaxes into the 3d' configuration. Deter- mine the term symbols of the new electron configuration. For each term symbol (level) that you find, determine: • The magnitude of the total angular momentum. The degeneracy of the level. c) Determine the magnitude (in J) of the splitting of the different levels of the 3d' configuration. Assume that hcĂ = 2.19 x 10-7- hcR, where R is the Rydberg constant and hcR is the Rydberg energy. d) The electron is in the lowest level of the 3d' configuration. Can the system relax to the 2p' 2Pa/2 level through emission of a photon?
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