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18 Einstein de Haas, Stern Gerlach, Zeeman, Lasers, MRI

18 Einstein de Haas, Stern Gerlach, Zeeman, Lasers, MRI -...

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Physics 13 Lecture 18 Prof. H. Gallagher 1 Plan for Today 1. Organization items 2. Angular momentum and magnetic fields 3. Spin 4. Experimental evidence and applications Einstein-de Haas experiment Stern-Gerlach experiment Zeeman effect Magnetic resonance imaging 5. Multi-electron atoms Spectroscopic notation The periodic table 6. Lasers
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Physics 13 Lecture 18 Prof. H. Gallagher Items There will be a special guest lecturer this Thursday, Prof. Fio Omenetto from the Department of Biomedical Engineering will describe his work in ultra-fast optics and biomedical applications. Next Tuesday there is no lecture. Next week there is no recitation or HW. Next Thursday (11/13) there is an exam! The exam will be held during class (4:30-5:45 pm) A notes page is allowed Constants will be provided like last time The exam will cover chapters 4-7 Exam 2 from 2006 with solution is available on Blackboard. 2
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Physics 13 Lecture 18 Prof. H. Gallagher 3 Hydrogen wave functions n : principal quantum numbers 1,2,3… l : angular momentum quantum number 0,1,2,…( n -1) m l : magnetic quantum number 0,±1,±2,…, ,± l ( m s : spin magnetic quantum number ±1/2 ) E n = 13.6 eV n 2 Orbital Spin Quantum Number l=0,1,2,…(n-1) s=1/2 Length of vector z component Magnetic quantum number m l =0,±1,±2,…, ,± l m s =±1/2 Magnetic moment L = l ( l + 1) S = 3/4 L z = m l S z = m s μ l = ( e /2 m ) L μ s = ( e / m ) S factor of 2 predicted by Dirac equation Orbital and intrinsic angular momentum are related to the magnetic properties of electrons / atoms. They can be studied by applying external magnetic fields (e.g. Stern-Gerlach expt)
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Physics 13 Lecture 18 Prof. H. Gallagher 4 Measuring angular momentum I ˆ n A current loop has a magnetic dipole moment: In a uniform magnetic field it will experience a torque that will align the moment with the magnetic field. In addition, for a non-uniform magnetic field the dipole experiences a net force. μ = IA ˆ n A U = μ B B μ
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Physics 13 Lecture 18 Prof. H. Gallagher Angular momentum and magnetism 1) Orbital motion of charges creates magnetic dipole moments. … there is a link between the magnetic properties of materials and the orbital motion of the electrons! --- Einstein-de Haas experiment 2) Magnetic dipole moments in an external magnetic field have potential energy that depends on the orientation between the dipole and the field. --- Zeeman effect 3) Magnetic dipoles will experience forces in non-uniform magnetic fields. --- Stern-Gerlach experiment 5
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