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Chapter 8: Q20CQ (page 338)

Question:Figure 8.16 shows that in the Z = 3 to 10 filling of the n = 2 shell (lithium to neon), there is an upward trend in elements' first Ionization energies. Why is there a drop as Z goes from 4 to 5, from beryllium to boron?

Short Answer

Expert verified

Answer

As the subshell 2p¹ is not closed, electrons in this shell could be removed with lesser ionization energy compared to beryllium.

Step by step solution

01

Explanation

It is easier with lesser ionization energy to remove the unpaired electron in the subshell2p¹ of Boron (B)than the electron in the closed subshellof Beryllium (Be)in the process of ionization energy from to L_i(z = 3 to 10).

02

Drop between 4 to 5

Beryllium has an electronic configuration . The subshells are closed. Electrons in the closed shells are very tightly bound and the positive nuclear charge is very large when compared to the negative charge of the inner shielding electrons. So, these electrons cannot be easily detached. So, higher energy is needed to remove these electrons, whereas, Boron has the electronic configuration $1 s^{2} 2 s^{2} 2 p^{1}$ . As the subshell is not closed, electrons in this shell could be removed with laser ionization energy compared to Beryllium.

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Most popular questions from this chapter

The Zeeman effect occurs in sodium just as in hydrogen-sodium's lone $3 s$ valence electron behaves much as hydrogen's 1.5. Suppose sodium atoms are immersed in a $0.1 T$ magnetic field.

(a) Into how many levels is the $3 P_{1 / 2}$ level split?

(b) Determine the energy spacing between these states.

(c) Into how many lines is the $3 P_{1 / 2}$ to $3 s_{1 / 2}$ spectral line split by the field?

(d) Describe quantitatively the spacing of these lines.

(e) The sodium doublet $(589.0 n m a n d 589.6 n m)$ is two spectral lines. $3 P_{3 / 2} \to 3 s_{1 / 2}$ and $3 P_{1 / 2} \to 3 s_{1 / 2}$ . 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?

Consider $Z = 19$ potassium. As a rough approximation assume that each of its $n = 1$ electron s orbits 19 pro. tons and half an electron-that is, on average, half its fellow $n = 1$ electron. Assume that each of its $n = 2$ electrons orbits 19 protons, two Is electrons. and half of the seven other $n = 2$ electrons. 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 of $a_{0}$ the orbit radii of hydrogenlike atoms of these effective Z,

(b) The radius of potassium is often quoted at around $0.22 nm$ . In view of this, are your $n = 1$ through $n = 3$ radii reasonable?

(c) About how many more protons would have to be "unscreened" to the $n = 4$ electron to agree with the quoted radius of potassium? Considering the shape of its orbit, should potassium's $n = 4$ electron orbit entirely outside all the lower-electrons?

Consider row 4 of the periodic table. The trend is that the $4 x$ subshell fills. Then the 3d, then the 4p.

(a) Judging by adherence to and deviation from this trend, whit might be said of the energy difference between the 4sand 3drelative to that between the 3dand 4p?

(b) Is this also true of row 5?

(c) Are these observations in qualitative agreement with Figure 8.13? Explain.

A Simple Model: The multielectron atom is unsolvable, but simple models go a long way. Section $7.8$ gives energies and orbit radii forone-electron/hydrogenlike atoms. Let us see how useful these are by considering lithium.

(a) Treat one of lithium's $n = 1$ electrons as a single electron in a one-electron atom ofrole="math" localid="1659948261120" $Z = 3$ . Find the energy and orbit radius.

(b) The other $n = 1$ electron being in the same spatial state. must have the same energy and radius, but we must account for the repulsion between these electrons. Assuming they are roughly one orbit diameter apart, what repulsive energy would they share, and if each claims half this energy. what would be the energies of these two electrons?

(c) Approximately what charge does lithium's lone valence electron orbit, and what radius and energy would it have?

(d) Is in reasonable to dismiss the role of the $n = 1$ electrons in chemical reactions?

(e) The actual energies of lithium's electrons are about $- 98 eV$ (twice, of course) and $- 5.4 eV$ . How good is the model?

(f) Why should the model's prediction for the valence electron's energy differ in the direction it does from the actual value?

Show that the symmetric and anti symmetric combinations of $(8 - 19)$ and $(8 - 20)$ are solutions of the two. Particle Schrödinger equation $(8 - 13)$ of the same energy as $ψ_{n} (x_{1}) ψ_{m} (x_{2})$ , the unsymmetrized product $(8 - 17)$ .

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