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Chapter 10: 7CQ (page 413)

For the four kinds of crystal binding – covalent, ionic, metallic, and molecular- how would the destiny of valence electrons vary throughout the solid? Would it be constant, centered on the atoms, or largest between the atoms? Or would it alternate, with a net charge density positive at one atom and negative at the next?

Short Answer

Expert verified

The valence electrons are strongly linked to the atoms in a molecular solid. As a result, the valence electron density will be concentrated around the atoms.

Step by step solution

01

Definitions of crystal bindin

All valence electrons are bound into bonds between neighboring atoms in a covalent solid. As a result, the valence electron density will be the highest among the atoms.

02

The destiny of valence electrons

Electrons are held from one side to the other in an ionic solid. When the ions with different signs alternate, the lowest energy state is reached. As a result, the density of valence electrons will alternate, with a positive net charge density on one ion and a negative charge density on its closest neighbors.

All atoms in a metallic solid share valence electrons. They combine to create an electron gas. As a result, the valence electron density remains constant.

The valence electrons are strongly linked to the atoms in a molecular solid. As a result, the valence electron density will be concentrated around the atoms.

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Most popular questions from this chapter

The accompanying diagrams represent the three lowest energy wave functions for three "atoms." As in all truly molecular states we consider, these states are shared among the atoms. At such large atomic separation, however, the energies are practically equal, so anelectron would be just as happy occupying any combination.

(a) Identify algebraic combinations of the states (for instance, 5+11/2+11/2 ) that would place the electron in each of the three atoms.

(b) Were the atoms closer together, the energies of states 1.11, and III would spread out and an electron would occupy the lowest energy one. Rank them in order of increasing energy as the atoms draw closer together. Explain your reasoning.

As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of 1. Because this "atom" is not in free space, however, the permitivity of free space, ε0. must be replaced by κε0, whereκ is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become

E=−me42(4πκε0)2ℏ21n2=−13.6eVκ2n2

Given κ=12for silicon, how much energy is needed to free a donor electron in its ground state? (Actually. the effective mass of the donor electron is less than , so this prediction is somewhat high.)

It is often said that the transistor is a basic element of amplification, yet it supplies no energy of its own. Exactly what is its role in amplification?

Of N2, O2 and F2, none has an electric dipole moment, but one does have a magnetic dipole moment, which one, and why?

(Refer to figure 10.10)

In section 10.2 , we discussed two-lobed Px.Pyand Pz states and 4 lobed hybrid sp3 states. Another kind of hybrid state that sticks out in just one direction is the sp , formed from a single p state and an s state. Consider an arbitrary combination of the 2s state with the 2pz state. Let us represent this bycosτψ2,0,0+sinτψ2,1,0(The trig factors ensure normalization in carrying out the integral , cross terms integrate to 0.leavingcos2τ∫|ψ2,0,0|2dv+sin2τ∫|ψ2.1.0|2dv. Which is 1.)

(a) Calculate the probability that an electron in such a state would be in the +z-hemisphere.(Note: Here, the cross terms so not integrate to 0 )

(b) What value of𝛕leads to the maximum probability, and what is the corresponding ratio ofψ2,0,0 andψ2,0,0 ?

(C) Using a computer , make a density (Shading) plot of the probability density-density versus r and𝛉- for the𝛕-value found in part (b).
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