This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: CHEM 356, Lecture 24, Fall 2009 1 Inuence of a Magnetic Field upon the Energy Levels of H. We consider the model of the H atom as an electron revolving around a proton in a circular orbit (essentially the Bohr model), and enquire about the electrodynamic consequences of this model of a moving charge. Magnetic Moment of the Electron. Let us begin by considering the motion of a charge ? around a closed loop of radius ? . A current owing around a loop that encloses an area constitutes a magnetic dipole moment of magnitude ? (m) = . If the charge ? moves around the loop at speed in uniform circular motion, it takes ? = 2 ?/ seconds to complete one loop, and since the current associated with this motion is given by = ? ? = ? 2 ? , while the enclosed area is = ? 2 , we have a scalar magnetic moment of ? (m) = 1 2 ?? . What about the vector form, since a dipole moment must have a vector character? We know that the position vector r is perpendicular to the velocity v for a circular loop, so that we can write a vector form for the dipole moment as (m) = 1 2 ? r v = 1 2 ? r p or (m) = ? 2 L . For an electron, we have charge ? = , and (m) = 2 e L . CHEM 356, Lecture 24, Fall 2009 2 Potential (Interaction) Energy. The potential energy of interaction of a magnetic dipole with a magnetic field B is given by field = (m) B . We normally choose B to lie along the axis (or, equivalently, to define the direction), so that we may write B = k , which allows us to write the classical form for the dipolefield interaction as field = ? (m) ? = 2 e ? , which is replaced in quantum mechanics by the operator field = 2 e ? . The Hamiltonian for the interaction of a magnetic dipole with an external magnetic field can be written in the form = + field = + field , or = + 2 e ?...
View
Full
Document
This note was uploaded on 02/28/2011 for the course CHEM 356 taught by Professor Prof.iaskjd during the Fall '09 term at Waterloo.
 Fall '09
 Prof.Iaskjd
 Electron, Proton

Click to edit the document details