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Chapter 8: Q19CQ (page 338)
Question: Early on, the lanthanides were found to be quite uncooperative when attempts were made to chemically separate them from one another. One reason can be seen in Figure 8.16. Explain.
Answer
They have similar ionization energies.
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Here we consider adding two electrons to two "atoms," represented as finite wells. and investigate when the exclusion principle must be taken into account. In the accompanying figure, diagram (a) shows the four lowest-energy wave functions for a double finite well that represents atoms close together. To yield the lowest energy. the first electron added to this system must have wave function and is shared equally between the atoms. The second would al so have function and be equally shared. but it would have to be opposite spin. A third would have function B. Now consider atoms far a part diagram(b) shows, the bumps do not extend much beyond the atoms - they don't overlap-and functions and approach equal energy, as do functions and . Wave functionsandin diagram (b) describe essentially identical shapes in the right well. while being opposite in the left well. Because they are of equal energy. sums or differences ofandare now a valid alternative. An electron in a sum or difference would have the same energy as in either alone, so it would be just as "happy" inrole="math" localid="1659956864834" , or- B. Argue that in this spread-out situation, electrons can be put in one atom without violating the exclusion principle. no matter what states electrons occupy in the other atom.
Consider potassium. As a rough approximation assume that each of itselectron s orbits 19 pro. tons and half an electron-that is, on average, half its fellowelectron. Assume that each of itselectrons orbits 19 protons, two Is electrons. and half of the seven otherelectrons. Continue the process, assuming that electrons at eachorbit a correspondingly reduced positive charge. (At each, an electron also orbits some of the electron clouds of higher. but we ignore this in our rough approximation.)
(a) Calculate in terms ofthe orbit radii of hydrogenlike atoms of these effective Z,
(b) The radius of potassium is often quoted at around. In view of this, are yourthroughradii reasonable?
(c) About how many more protons would have to be "unscreened" to theelectron to agree with the quoted radius of potassium? Considering the shape of its orbit, should potassium'selectron orbit entirely outside all the lower-electrons?
Were it to follow the standard pattern, what would be the electronic configuration of element 119.
Question: The “radius of an atom” is a debatable quantity. Why?
Suppose that the channel’s outgoing end is in the hydrogen Stem-Gerlach apparatus of the figure. You place a second such apparatus whose channel is aligned with the first but rotated about the -axis, so that its B –field lines point roughly in the -direction instead of the. What would you see emerging at the end of your added apparatus? Consider the behavior of the spin-up and spin-down beams separately. Assume that when these beams are separated in the first apparatus, we can choose to block one or the other for study, but also assume that neither deviates too far from the center of the channel.
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