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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

Show that for a room-temperature semiconductor with a band gap of 1eV, a temperature rise of 4K would raise the conductivity by about 30%.

The bond length of theN2molecule is 0.11nm, and its effect the spring constant is 2.3×103N/m .

(a) From the size other energy jumps for rotation and vibration, determine whether either of these modes of energy storage should be active at 300K .

(b) According to the equipartition theorem, the heat capacity of a diatomic molecule storing energy in rotations but not vibrations should be52R(3 translational +2rotational degrees of freedom). If it is also storing energy in vibrations. it should be72R(adding 2 vibrational degrees). Nitrogen's molar heat capacity is 20.8J/mol.K at 300K. Does this agree with your findings in part (a)?

Question: The critical temperature lead is 7.2 K. What is the binding energy of its Cooper pairs at zero temperature?

The diagram shows a bridge rectifier circuit. A sinusoidal input voltage is fed into four identical diodes. each represented by the standard diode circuit symbol. The symbol indicates the direction of conventional current flow through the diode. The plots show input and output voltages versus time. Note that the output voltage is strictly in one direction. Explain

(a) how this circuit produces the unidirectional output voltage it does, and

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(a) Prove that the ratio ofFTto the object's acceleration is negative. (Note: This object can't roll without slipping unless there is friction.) You can do this by actually calculating the acceleration from the translational and rotational second la was of motion, but it is possible to answer this part without such a "real" calculation.

(b) Verify thatFTtimes the speed at which the string moves in the direction of FT (i.e., the power delivered byFT) equals the rate at which the translational and rotational kinetic energies increase. That is.FTdoes all the work in this system, while the "internal" force does none. (c) Briefly discuss how parts (a) and (b) correspond to behaviors when an external electric field is applied to a semiconductor.
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