DQ8D_solution - Discussion Challenge 8D P212, Week 8...

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Discussion “Challenge ” 8D P212, Week 8 Magnetic Dipoles in Atomic Physics Here is one reason that we are studying magnetic dipole moments: nature is filled with current loops at the atomic and subatomic levels! Magnetic dipoles appear constantly in those fields of physics. Consider the hydrogen atom = one proton (charge + e ) with an electron (charge – e ) orbiting around it. As you know, the electron can live in a number of “orbitals”, which are states with different orbital angular momentum L . From quantum mechanics, we know that L of an electron in such an orbital is L = l = where l is a “quantum number” that takes only integer values: 0, 1, etc. Further, the electron has spin angular momentum S , where S = s = . For an electron, s is always 1/2. You may think of spin this way: the electron is constantly revolving around its own internal axis, producing a constant angular momentum = /2. The diagram shows a hydrogen atom in a “d-state” with l = 2. Both the spin S and orbital angular momentum L are pointing upwards (+ z ) in the figure, but that doesn’t have to be the case. We’ll consider 4 states: ↑↑ , ↓↓ , ↑↓ , and ↓↑ . We’ll use the first, thick arrow to refer to L (since it is bigger than S ), so ↑↑ means l z = +2, s z = +1/2, while ↓↑ means l z = -2, s z = +1/2, etc. 1 As it happens, any rigid charged body that is either orbiting or spinning has a magnetic dipole moment that is proportional to its angular momentum. The electron’s intrinsic magnetic moment (due to its spin) is µ s = µ B , where µ B = 9.3 x 10 -24 J/T is a physical constant called the “Bohr magneton”. The orbital motion of the electron also produces a magnetic moment: µ l = l µ B (a) Given the spin and orbital directions shown in the figure, in which directions do the magnetic moments µ s and µ l point? Don’t forget the electron has a negative charge. Draw them on the figure.
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This note was uploaded on 06/16/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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DQ8D_solution - Discussion Challenge 8D P212, Week 8...

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