Consider the He atom. It has 2 electrons, each with its own spin,

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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; mS = -1, 0, +1 (B) S = -1, 0 or 1; mS = -1, 0, +1 (C) S = 0; mS = 0 (D) S = 1; mS = -1, 0, +1 (E) S = 1; mS = 0, 1 z z z

OR 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; mS = -1, 0, +1 (B) S = -1, 0 or 1; mS = -1, 0, +1 Wrong, because S ≥ 0 ! (C) S = 0; mS = 0 Wrong, because the vectors can add (D) S = 1; mS = -1, 0, +1 Wrong, because the vectors can cancel (E) S = 1; mS = 0, 1 Wrong, because the vectors can add, and because m goes from –S to S z z z 1 ħ 0.5 ħ + = 0.5 ħ 0.5 ħ OR z z z 0.5 ħ + = -0.5 ħ 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)