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Chapter 8: Q1CQ (page 338)
A dipole without angular momentum can simply rotate to align with the field (through it would oscillate unless it could shed energy). One with angular momentum cannot. Why?
If it already has angular momentum along the plane, then the change in angular momentum will also be the plane.
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The Zeeman effect occurs in sodium just as in hydrogen-sodium's lone valence electron behaves much as hydrogen's 1.5. Suppose sodium atoms are immersed in amagnetic field.
(a) Into how many levels is thelevel split?
(b) Determine the energy spacing between these states.
(c) Into how many lines is thetospectral line split by the field?
(d) Describe quantitatively the spacing of these lines.
(e) The sodium doublet is two spectral lines.and. which are split according to the two differentpossible spin-orbit energies in the 3Pstate (see Exercise 60). Determine the splitting of the sodium doublet (the energy difference between the two photons). How does it compare with the line splitting of part (d), and why?
The radius of cesium is roughly.
(a) From this estimate the effective charge its valence electron orbits
(b) Given the nature of the electron's orbit. is this effective nuclearcharge reasonable?
(c) Compare this effective Zwith that obtained for sodium in Example 8.3. Are the values at odds with the evidence given in Figurethat it takes less energy to remove an electron from cesium than from sodium? Explain.
(a) To determine the repulsive energy between the two electrons in helium.
(b) To determine the distance of electrons that would have to be separated.
(c) To compare distance with approximate orbit radius in Z=2hydrogen like atom.
Question: As indicated to remove one of the helium’s electrons requires of energy when orbiting ? Why or why not?
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).
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