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Chapter 10: Q55E (page 470)

Carry out the integration indicated in equation (10.10)

Short Answer

Expert verified

The integration is obtained and proved.

Step by step solution

01

Determine the formulas

Consider the formulato determine the thermal energy as:

E=knT ….. (1)

Here,kn is Boltzmann constant and the temperature is T.

02

Solve for the integration as:

Solve for the integration as:

Nexcited=∫EF+12Egap∞1e(E−EF)/knT+1DdE

Considerx=EknT then,dx=dEknT .

Consider xF=EFknTandxgap=EgapknT

Substitute the values in the integration and solve as:

Nexcited=DkBT∫xF+12xgap∞1exF−xgap+1dx=DkBT∫xF+12xgap∞exF−xgapexF−xgap+1dx

Solve for the derivative of the function as:

dln(1+exf−xgap)dx=11+exf−xexp−x(−1)

Solve the integration further as:

Nexcited=−DkBTln(1+exF−x)xF+12gap∞=DkBTln(1+eEgap2kBT)

Hence, the integration is obtained and proved.

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Most popular questions from this chapter

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?

What is Cooper pair, and what role does it play in superconductivity?

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?

Question: Referring to equations(10-2), lobe I of the hybrid states combines the spherically symmetric s state with the state that is oriented along thez-axis. and thus sticks out in the direction (see Exercises 28 and 33), If Figure is a true picture, then in a coordinate system rotated counterclockwise about they-axis by the tetrahedral angle, lobe II should become lobe. In the new frame. -values are unaffected. but what had been values in the 2x -plane become values in the -plane. according tox=x'cosα+z'sinα and z'cosα-x'sinα, whereα=109.5o iscos-1(-13) , or .

(a) Show that lobe II becomes lobe I. Note that since neither the 2s state nor the radial part of the p states is affected by a rotation. only the angular parts given in equations (10-1) need be considered.

(b) Show that if lobe II is instead rotated about thez-axis by simply shifting φby±1200 . it becomes lobes III and IV.

Question: Volumes have been written on transistor biasing, but Figure 10.45 gets at the main idea. Suppose that and that the "input" produces its own voltage . The total resistance is in the input loop, which goes clockwise from the emitter through the various components to the base, then back to the emitter through the base-emitter diode. this diode is forward biased with the base at all times 0.7 V higher than the emitter. Suppose also that Vcc = 12 V and that the "out- put" is350KΩ . Now. given that for every 201 electrons entering the emitter, I passes out the base and 200 out the collector, calculate the maximum and minimum in the sinusoidally varying

(a) Current in the base emitter circuit.

(b) Power delivered by the input.

(c) Power delivered to the output.

(d) Power delivered byVce.

(e) what does most of the work.
See all solutions

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