Consider the He atom. It has 2 electrons, each with its own spin, and. Adding spin angular momenta means adding vectors. With this in mind, what are the.

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Quantum Theory and the Electronic Structure of Atoms

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Presentation transcript:

Consider the He atom. It has 2 electrons, each with its own spin, and. Adding spin angular momenta means adding vectors. With this in mind, what are the total spin quantum numbers of this system? Remember that spin is a form of angular momentum (A) S = 0 or 1;m S = -1, 0, +1 (B) S = -1, 0 or 1; m S = -1, 0, +1 (C) S = 0;m S = 0 (D) S = 1; m S = -1, 0, +1 (E) S = 1; m S = 0, 1 z z z

Consider the He atom. It has 2 electrons, each with its own spin, and. Adding spin angular momenta means adding vectors. With this in mind, what are the total spin quantum numbers of this system? Remember that spin is a form of angular momentum (A) S = 0 or 1;m S = -1, 0, +1 (B) S = -1, 0 or 1; m S = -1, 0, +1 Wrong, because S ≥ 0 ! (C) S = 0;m S = 0 Wrong, because the vectors can add (D) S = 1; m S = -1, 0, +1 Wrong, because the vectors can cancel (E) S = 1; m S = 0, 1 Wrong, because the vectors can add, and because m goes from – S to S z z z + = 0.5 ħ 1 ħ z z z + = 0.5 ħ -0.5 ħ OR vectors cancel!

As a general rule, we cannot distinguish one particular electron from another (can’t fix labels on them). If electrons are indistinguishable, which of the spin configurations is incorrect? (A)  Spin (1,2) =  (1)  (2) (B)  Spin (1,2) =  (1)  (2) (C)  Spin (1,2) =  (1)  (2) (D)  Spin (1,2) =  (1)  (2) +  (1)  (2) (E)  Spin (1,2) =  (1)  (2) -  (1)  (2)

As a general rule, we cannot distinguish one particular electron from another (can’t fix labels on them). If electrons are indistinguishable, which of the spin configurations is invalid? (A)  Spin (1,2) =  (1)  (2) (B)  Spin (1,2) =  (1)  (2) (C)  Spin (1,2) =  (1)  (2)we would have to know which one points up and which points down (D)  Spin (1,2) =  (1)  (2) +  (1)  (2) (E)  Spin (1,2) =  (1)  (2) -  (1)  (2)