Chapter 8: Q50E (page 342)
Determine the expected valence of the element with atomic number 117.
The expected valence of the element with atomic numberis or .
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Question: Lithium is chemically reactive. What if electrons were spin instead of spin. What value of Z would result in an elements reactive in roughly the same way as lithium? What if electrons were instead spin-1?
Question: In classical electromagnetism, the simplest magnetic dipole is a circular current loop, which behaves in a magnetic field just as an electric dipole does in an electric field. Both experience torques and thus have orientation energies -p.Eand(a) The designation "orientation energy" can be misleading. Of the four cases shown in Figure 8.4 in which would work have to be done to move the dipole horizontally without reorienting it? Briefly explain. (b) In the magnetic case, using B and u for the magnitudes of the field and the dipole moment, respectively, how much work would be required to move the dipole a distance dx to the left? (c) Having shown that a rate of change of the "orientation energy'' can give a force, now consider equation (8-4). Assuming that B and are general, writein component form. Then, noting thatis not a function of position, take the negative gradient. (d) Now referring to the specific magnetic field pictured in Figure 8.3 which term of your part (c) result can be discarded immediately? (e) Assuming thatandvary periodically at a high rate due to precession about the z-axis what else may be discarded as averaging to 0? (f) Finally, argue that what you have left reduces to equation (8-5).
Using to eliminate L - S. as wellas , obtain equation (8- 32 )from the equation that precedes it.
Verify that the normalization constant given in Example 8.2is correct for both symmetric and antisymmetric states and is independent ofand ?
The Slater determinant is introduced in Exercise 42. Show that if states and of the infinite well are occupied. with the particle in state being spin up and the one in being spin down. then the Slater determinant yields the antisymmetric multiparticle state: .
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