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Chapter 10: Q54E (page 470)

Section 10.6 notes that as causes of resistance, ionic vibrations give way to lattice imperfections at around 10 K. A typical spring constant between atoms in a solid is or order of magnitude103 Nm and typical spacing is nominally10-10 m . Estimate how much the vibrating atoms locations might deviate, as a function of their normal separations, at 10 K.

Short Answer

Expert verified

The vibrational distance is only 0.5%of the nominal separation.

Step by step solution

01

 Step 1: Determine the formulas

Consider the formulato determine the thermal energy as:

E=knT ….. (1)

Here, knis Boltzmann constant and the temperature is T.

Consider the expression for the vibrational distance as:

x=2(spring potential energy)κ

02

Determine the number of vibrating atoms locations that might deviate.

From equation (1) solve for the thermal energy as:

ET=(1.38×10−23 JK)(10 K)=1.38×10−22 J

Solve for the expression for the vibrational energy as:

x=2(1.38×103)103 Nm=5×10−23 m

Solve for the ratio of the distance as:

xa=5×10−2310−10=0.5%

Therefore, the vibrational distance is0.5% only of the nominal separation.

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Most popular questions from this chapter

Exercise 29 outlines how energy may be extracted by transferring an electron from an atom that easily loses an electron from an atom that easily loses an electron to one with a large appetite for electrons , then allowing the two to approach , forming an ionic bond.

  1. Consider separately the cases of hydrogen bonding with fluorine and sodium bonding with fluorine in each case , how close must the ions approach to reach “break even” where the energy needed to transfer the electron between the separated atoms is balanced by the electrostatic potential energy of attraction? The ionization energy of hydrogen is 13.6 eV , that of sodium is 5.1 eV , and the electron affinity of fluorine is 3.40 Ev.
  2. Of HF and NaF , one is considered to be an ionic bond and the other a covalent bond . Which is which and Why?

Sketch an energy-versus-position diagram. Complementary to Figure 10.4, showing valence hole motion a conduction electron participation in an operating pnp transistor.

The "floating magnet trick" is shown in Figure 10.50. If the disk on the bottom were a permanent magnet, rather than a superconductor, the trick wouldn't work. The superconductor does produce an external field very similar to that of a permanent magnet. What other characteristic is necessary to explain the effect? (Him: What happens when you hold two ordinary magnets so that they repel, and then you release one of them?)

It takes less energy to dissociate a diatomic fluorine molecule than a diatomic oxygen molecule (in fact, less than one-third as much). Why is it easier to dissociate fluorine?

why is covalent bonding directional, while ionic bonding is not?
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